Thermal Conductivity Of Liquids

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Content This dissertation has been
microfilmed exactly as received 6 8-13,581
MALLAN, George Martin, 1935-
THERMAL CONDUCTIVITY OF LIQUIDS,
University of Southern California, P h .D ., 1968
Engineering, chem ical
University Microfilms, Inc., Ann Arbor, Michigan
THERMAL CONDUCTIVITY OF LIQUIDS
by
George Martin Malian
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
Doctor of Philosophy
(Chemical Engineering)
June 1968
UNIVERSITY O F SO U TH ER N CALIFORNIA
TH E GRADUATE SC H O O L
UNIVERSITY PARK
LOS ANGELES. CA LIFOR N IA 9 0 0 0 7
This dissertation, written by
GEORGE MARTIN M ALLAN
under the direction of his....Dissertation Com
mittee, and approved by all its members, has
been presented to and accepted by the Graduate
School, in partial fulfillment of requirements
for the degree of
D O C T O R O F P H I L O S O P H Y
Dean
Date June,....1968.
DISSERTATION CO M M ITTEE
iC,
Chairman
.
V
THIS WORK IS DEDICATED
TO
JUDITH ENGLAND
ii
ACKNOWLEDGMENTS
The author would like to express his appreciation
to the following individuals for their aid and encourage
ment :
Dr. F. J. Lockhart--for his interest, encouragement
and guidance during the course of the research;
The members of the Research Committee: Dr. C. J.
Rebert and Professor R. L. Mannes;
Mrs. Ruth Toyama--for her preparation of the rough
draft and for her gentle encouragement over the entire
graduate period.
Mrs. Erna Lemberger-- for her preparation of the
final manuscript.
The Marquardt Corporation--for offering part-time
employment during the important period of data
collection.
iii
TABLE OF CONTENTS
Page
DEDICATION......................................... ii
ACKNOWLEDGMENTS ..................................... iii
LIST OF T A B L E S ..................................... vii
LIST OF FIGURES .................................. ix
Chapter
I. INTRODUCTION .............................. 1
II. EXISTING THERMAL CONDUCTIVITY DATA . . . 7
A. Existing Data....................... 7
B. Existing Apparatus ................ 9
C. Choice of Liquids for Correlation
Studies........................... 16
III. TRANSIENT HOT-WIRE APPARATUS AND THE
COLLECTION OF EXPERIMENTAL THERMAL
CONDUCTIVITY D A T A ....................... 18
A. Background.......................... 18
B. Description of Apparatus......... 19
C. Proof of Apparatus and Collection
of D a t a ............................ 28
IV. PREDICTION FOR THE THERMAL CONDUCTIVITY
OF LIQUIDS AT 77° F ..................... 32
A. Existing Correlations of k vs. T. . 32
B. The Robbins and Kingrea Estimation
for Liquid Thermal Conductivity
vs. Temperature ................ 35
C. The Modified Weber Equation for
the Prediction of the Thermal
Conductivity of Non-Polar Liquids
at 77° F
iv
V
Chapter Page
D. Correlation for the Deviation of
Polar Liquids from the Predictions
of the Modified Weber Equation at
77° F .............................. 41
V. PREDICTION FOR THE TEMPERATURE DEPENDENCY
OF THERMAL CONDUCTIVITY AT 77° F .... 51
A. The Horrocks-McLaughlin Relationship. 53
B. Correlation for the Deviation of
Polar Liquids from the H-M
Relationship ....................... 55
C. Accuracy of the Predicted Tempera
ture Dependency of Thermal
Conductivity ....................... 62
VI. DISCUSSION OF THE CORRELATING PARAMETERS. . 67
A. Everett's Entropy of Vaporization,
A S * .................................. 69
B. The Dielectric Constant, £ ......... 77
C. The Dipole Moment, y, and Density
Ratio p/ph q ....................... 80
VII. CONCLUSIONS.................................. 87
APPENDICES
A. DESCRIPTION OF THE TRANSIENT HOT-WIRE
THERMAL CONDUCTIVITY APPARATUS 91 "
B. GRAPHICAL PRESENTATION OF EXPERIMENTAL
RESULTS FOR THE THERMAL CONDUCTIVITY
OF L I Q U I D S ..................................... 108
C. IDENTIFICATION OF COLUMNS IN THE FOLLOWING
TABLES OF EXPERIMENTAL AND CALCULATED
D A T A ............................................ 138
D. PHYSICAL PROPERTIES REQUIRED FOR THE
PREDICTION OF k AND dk/dt..................... 156
E. OUTLINE OF TRIAL-AND-ERROR PROCESS FOR OB
TAINING CORRELATIONS $ AND 0 FOR THE
DEVIATIONS OF POLAR LIQUIDS ................ 162
vi
Chapter Page
(APPENDICES)
F. DEGREE OF MOLECULAR ASSOCIATION OF SOME
LIQUIDS AS A FUNCTION OF TEMPERATURE . . .168
BIBLIOGRAPHY ........................................... 173
LIST OF TABLES
Table Page
1-1 Table of Liquids Investigated .............. 5
11 -1 Summary of Existing Thermal Conductivity
Apparatus (conducted by Jamieson and
Tudhope in 1963 (27) ) 11
II-2 Experimental Results for the Thermal Con
ductivity of Toulene at 20° C ........... 14
III-1 Summary of Experimental Results at
100 psig. ................................ 30
IV-1 Experimental and Predicted Thermal Conduc
tivities for the Non-Polar Liquids
at 77° F .................................. 42
IV-2 Deviation of Polar Liquids from the Predic
tions of the Modified Weber Equation
IV- 3 at 77° F ............................. 44
IV-3 Prediction for the Thermal Conductivity of
Liquids at 77° F by Equation IV-4 .... 49
C In )
(Appendices)
C-l Table of Experimental and Calculated
D a t a ..........................................141
D-1 Physical Properties of the Liquids at
77° F ..........................................158
D-2 References for Physical Properties .... 161
F-l Alcohols of Constant Molecular Association
as Reported by L. H. Thomas, J. Chem.
Soc., 1948, 1345
vii
viii
Table Page
F-2 Molecular Association vs. Temperature
Data as Reported by L. H. Thomas,
J. Chem. Soc. (Lon.) 1960, 4906 ......... 170
F-3 Degree of Molecular Association of m-Cresol
vs. Temperature........................... 171
LIST OF FIGURES
Figure Page
111 -1 Temperature Rise in Hot-Wire Element
vs. T i m e ................................. 23
111 - 2 Transient Hot-Wire Thermal Conductivity
Apparatus.................................. 25
IV-1 Correlation for the Deviation of Polar
Liquids from the Predicted k Values
of the Modified Weber Equation at
77° F ..................................... 47
V-l Horrocks-McLaughlin Relationship and Non-
Polar Liquids.............................. 56
V-2 Deviations of Polar Liquids from the
Horrocks-McLaughlin Relationship .... 58
V-3 Correlation for the Deviation of Polar
Liquids from the Horrocks-McLaughlin
Relationship .............................. 60
V-4 Percent Error in Predicted Thermal Conduc
tivities as a Function of Temperature
above Reference Point .................. 63
V-5 Percent Error in Predicted k vs. T Using
Calculated k as the Reference Point . . . 66
VI-1 Definition and Notation of Entropies
of Vaporization ......................... 71
VI-2 Possible Association of Acetic Acid .... 83
ix
X
Figure Page
C In )
(Appendices)
A-l Thermal Conductivity Cell and Pressure
System..................................... 93
A-2 Transient Hot-Wire Apparatus for the
Measurement of Liquid Thermal Con
ductivities .............................. 96
A-3 Series of Actual X-Y Data Recordings for
Toluene at 95° F ......................... 99
A-4 Thermal Conductivity of T o l u e n e............ 100
A-5 Calibration of Cell #1, Iridium Set #3 . . 102
F-l Degree of Molecular Association of
m-Cresol.................... 172
CHAPTER I
INTRODUCTION
The thermal conductivity of any substance is usu
ally defined by Fourier's empirical description of heat
conduction which can be stated differentially as
. ^ Pq t.i
d6 A dx bq. 1 i
where dQ is the quantity of heat transmitted in time d0
along a temperature gradient dt/dx perpendicular to an
area A. The proportionality constant, k, is then the
thermal conductivity of any substance.
The thermal conductivity of a liquid is a physical
property which is important in both theoretical and prac
tical engineering considerations. As a molecular trans
port property, its theoretical importance in energy
transfer parallels that of viscosity in momentum transfer
and diffusivity in mass transfer. In practical engineer
ing applications, thermal conductivity is employed along
with other physical properties in dimensionless equations
of heat transfer which are in daily use. The generalized
equations for predicting film coefficients for the heating
and cooling of liquids in turbulent flow show that this
coefficient h is proportional to the 0.7 power of the
thermal conductivity k. Equations for predicting two-
phase heat transfer film coefficients show that h is
proportional to the 0.75 or 1.0 power of the liquid
thermal conductivity k.
Despite the importance of knowing a liquid's
thermal conductivity, there exists a genuine scarcity of
reliable experimental data which can be used for applica
tions at even ordinary temperature levels. This paucity
of data is directly attributed to the difficulty of
measuring this thermal property with a reasonable degree
of precision. For this reason, it has been attractive
for investigators in this field of study to attempt to
correlate the meager results available in order to accom
modate the needs of the scientific and engineering
communities. Most of the correlations presented prior to
1962 are rather inaccurate for the great majority of
fluids and, at best, apply to only a narrow class of non
polar liquid hydrocarbons. It was not until the work of
Robbins and Kingrea in 1962 (54)* that a correlation was
published which fairly accurately predicts the values for
Numbers in parenthesis refer to numbered items in
the Bibliography.
polar as well as non-polar liquids. These authors were
handicapped, however, by both the paucity of reliable
thermal conductivity data which existed at the time and
the necessity of several rather questionable constants
which were employed to account for the behavior of most
polar liquids.
At the time Robbins and Kingrea published their
correlation, reliance had to be placed upon experimen
talists who were gathering thermal conductivity data
from very slow and cumbersome steady-state devices.
The best experimental output from these devices was often
only a single data point for a full day's effort. Na
turally, the quantity of data available for correlation
was not too extensive and furthermore the data which
existed for many liquids often differed by as much as
20%, with almost no guide as to which value was more
correct.
The general scarcity of reliable liquid thermal
conductivity data should be eliminated with the advent
of fast and accurate transient hot-wire apparatus, the
first of which was introduced by P. Grassmann in 1960
(18, 19). The employment of these devices enables experi
mentalists to obtain reliable data from ten to twenty times
faster than was possible with the older steady-state type.
The work presented in this dissertation covers
three areas in the field of liquid thermal conductivity:
1. Experimental thermal conductivity data were
collected on 23 liquids as a function of temperature by
using a transient hot-wire apparatus similar to that
proposed by Grassmann. In addition to the first-hand
experimental data, reliable literature values were also
obtained for 33 additional liquids by using the work of
only a selected number of experimentalists of proven
ability. Fairly reliable values were thus obtained for
the 56 liquids listed in Table 1-1 and these data comprise
the basis for the correlations presented.
2. A correlation is presented for the prediction
of the thermal conductivity of liquids at 77° F. This
correlation is based upon a modification of the empirical
Weber equation to which a corrective term is added to
account for the deviation of most polar liquids. The
corrective term is general for all liquids and is dependent
upon the associative and polar properties of the liquid.
The correlation is accurate to an average 3.3% for 31 out
of the 38 liquids listed in Table 1-1 for which correlat
ing parametric data are available. The errors for the
remaining seven liquids are large and range from 11 to
36% .
3. A correlation is also presented for the pre
diction of the temperature dependency of thermal conduc
tivity. This correlation is based upon the theoretical
T A B L E 1-1
T a b le of L iq u id s In v e s tig a te d
5
# L iq u id
T h e r m a l
Cond.
R ef.
# L iquid
T h e r m a l
C ond.
R ef.
1 n - P e n t a n e R ie d e l
30
2 - N itr o p r o p a n e M a lia n
2 C y c lo p e n ta n e S a k ia d is 31
N itr o b e n z e n e M a lia n
3 n -H e x a n e M a lia n 32 m - N i t r o t o l u e n e M a lia n
4 C y c lo h e x a n e H o r r o c k s 33 B e n z o n itr ile M a lia n
5 2 -M e th y lp e n ta n e S ak ia d is 34 C a r b o n -
6 2, 3 - D im e t h y l-
t e t r a c h l o r i d e M a lia n
butane S a k ia d is 35. C h lo r o f o r m J a m i e son
7 Me thy 1- 36
Io d o b en ze n e R ie d e l
c y c lo p e n ta n e S a k ia d is ' 37
B r o m o b e n z e n e R ie d e l
8 Me thy 1- 38 E th y lio d id e R ie d e l
c y c lo h e x a n e M a lia n 39 E t h y lb r o m i d e R ie d e l
9 n -H e p ta n e M a lia n 40
1, 2 - D ic h lo r o -
10 n - O c ta n e
F ilip p o v e th a n e R ie d e l
S a k ia d is 41 T r i c h l o r o -
11 n -N o n a n e S a k ia d is e th y le n e R ie d e l
12 n - D e c a n e M alian 42 T e t r a c h l o r o -
13 B en ze n e R ie d e l eth y len e M a lia n
14 M e th a n o l J o b s t 43 F o r m i c A cid
J o b s t
15 E th a n o l J o b s t 44 A c e tic A cid
J o b s t
16 n - P r o p a n o l J o b s t 45 n - B u t y r i c A c id J o b s t
17 n - B u ta n o l J o b s t 46
1, 3 - B u ta n e d io l M a lia n
18 C y c lo h e x a n o l M a lia n 47 1, 4 - B u ta n e d io l M a lia n
19 A c e ta ld e h y d e J o b s t 48 N, N - D i e m e t h y l -
2 0 n - P r o p i o a l d e h y d e J o b s t
f o r m a m i d e M a lia n
21 n - B u tr a l d e h y d e J o b s t 49 N, N - D i m e th y l -
22 F u r f u r a l S c h m id t a c e t a m i d e M a lia n
23 A ceto n e R ie d e l 50
N - M e th y la c e ta m id e M alia n
24 M e t h y l - E t h y l - 51 D u P o n t Oil M a lia n
K etone J o b s t 52 G u lf H a r m o n y #204 M a lia n
25 W a te r P o w e l l 53 C h e v r o n A lta
26 H e a v y W a te r V e n a r t V is 530 M a lia n
27 E th y le n e g ly c o l
G r a s s m a n n 54 G u lf O il #896
M a lia n
28 P r o p y l e n e g lycol M a lia n 55 S h e ll P r e m .
29 G ly c e r o l M a s o n Die s e lin e
M a lia n
56
C h e v r o n D ie s e l Fuel M a lia n
relationship of Horrocks and McLaughlin (24) which is
shown to be correct for non-polar liquids. A general
corrective term has been added to account for the
deviation of most polar liquids and is composed of the
same associative and polar properties which were used in
the previous correlation. The correlation for the tem
perature dependency predicts the thermal conductivity at
277° F for 36 out of the 39 liquids of Table 1-1 for
which parametric data are available, to an average
accuracy of 3.5% when experimental data at 77° F are used
as the reference point. The three liquids which could
not be correlated are in the carboxylic acid group
(Nos. 43, 44, 45). These liquids are believed to deviate
because of molecular association which persists in the
vapor phase. Reasons for this belief are to be found in
Chapter VI.
CHAPTER II
EXISTING THERMAL CONDUCTIVITY DATA
A. Existing Data
In the field of liquid thermal conductivities, few
experimentalists have reported on more than five to ten
liquids at a time. The scarcity of comprehensive data
is compounded by the inherent difficulty in conducting
precise measurements with the older steady-state types
of apparatus. The result has been that the literature
contains many values for the same liquids which are often
10 to 20% in disagreement. Investigators interested in
correlating existing data have had considerable problems
in choosing the most reliable values from the somewhat
meager results available.
About ten years ago, a substantial quantity of
data was published by Sakiadis and Coates (5-S, 56).
Nearly all correlations published since that time have
relied heavily upon the experimental results of these
authors. Unfortunately, these values are from 5 to 10%
higher than data reported by several other highly respected
7
experimentalists. The weight of evidence to date indicates
that the lower thermal conductivity values are more nearly
correct.
A picture can be gained of the general paucity of
thermal conductivity versus temperature data by referring
to the literature surveys conducted during the past
fifteen years (27, 39, 55). The best known of these works
was published in 1952 by Sakiadis and Coates (55) . These
authors, however, were handicapped by the genuine lack
of data existing at that time. In addition, they
attempted to grade the reliability of the various in
vestigators, but based their system upon the sixteen most
reliable values published in the International Critical
Tables. These ICT values of 1927 have been largely dis
credited at the present time. A comprehensive survey
with a reliable grading system was published by Jamieson
and Tudhope in 1963 (27) . These authors were able to list
thermal conductivity values for 275 pure organic liquids.
The great majority of these values, however, are not con
sidered by the authors themselves to be reliable. If
temperature versus thermal conductivity data are required,
this survey was able to list only 66 liquids for which
at least two investigators reported results. For many
of these liquids, the reported temperature dependencies
differed by as much as 30 to 50%. More reliability can
often be gained if at least three different investigators
reported results for the same liquid, but such data are
listed for only 41 liquids.
Almost all the data listed in past literature
surveys have been reported by investigators using some
type of slow, steady-state thermal conductivity apparatus.
Each type has inherent sources of error and most of these
have been well documented in the work published by Tate
and Hill in 1964 (63). The predominant error, however,
is natural convection and this occurs to varying degrees
in all experimental determinations. It is believed that
the large scatter in data reported by the various sur
veys is due not so much to the different types of
apparatus, but to the inherent difficulty in operating
the older steady-state types of thermal conductivity
devices.
B. Existing Apparatus
Experimental measurements on the thermal conduc
tivity of liquids have been conducted since 1839 when
Depretz (13) first set up a parallel plate apparatus in
which an upper circular plate was maintained as a
constant heat source and a lower plate acted as a heat
sink. The heat flux thus generated across a liquid layer
between these plates was proportional to the liquid's
thermal conductivity as defined by Fourier's relation
ship (Eq. 1-1). Any apparatus which can supply tractable
10
boundary conditions for Eq. 1-1 is suitable for the
generation of measurable data. Since a solution for
Fourier’s equation requires data for heat flux dQ/d0 as
well as the temperature distribution dt/dx, most experi
mentalists have employed steady-state devices in order to
insure constant values for both dQ/d0 and dt/dx. The most
common apparatus continues to be the parallel plate type;
however, long concentric cylinders offer the advantage
of lessening the possibility of heat leaks around the
edges while concentric spheres reduce this problem even
further.
In the survey of liquid thermal conductivities
published by Jamieson and Tudhope (27), the authors
listed data reported by 59 different investigators, 53 of
which used some type of steady-state apparatus. A summary
of these apparatus is given in Table II-l.
Of the 53 investigators who used the steady-state
mode of operation, 16 employed a hot-wire as their heat
source. This type is a variation of the concentric
cylinder approach where the constant heat flux is deter
mined by the amount of current which passes through the
immersed wire. The temperature distribution can be
measured by either suspending thermocouples in the sur
rounding liquid or embedding them in a surrounding
cylinder of metal. All of the devices summarized in
Table II-l have minor sources of error peculiar to the
TABLE II-l
S u m m a r y of E x is tin g T h e r m a l C o n d u c tiv ity A p p a r a tu s
(co n d u c te d by J a m i e s on and Tudhope in 1963 (27))
Type * of T h e r m a l No, of I n v e s ti g a to r s
C o n d u c tiv ity A p p a r a tu s to U se T ype______
P - S - A 16
P - S - R 2
C - S - A 10
C - S - R 7
S -S -A 2
W -S -R 10
W -S -A 6
W - T - R 1
W - T - A 5
59
* ls t l e t t e r r e f e r s to g e o m e t r y of h e a t s o u r c e - h e a t sin k
a r r a n g e m e n t :
P - p a r a l l e l p la te s
C - c o n c e n tr ic c y l i n d e r s
S - c o n c e n tr ic s p h e r e s
W - h o t - w i r e s u r r o u n d e d by liquid
2nd l e t t e r r e f e r s to m o d e of o p e ra tio n :
S - s t e a d y - s t a t e
T - t r a n s i e n t
3 rd l e t t e r r e f e r s to the m e th o d of c a lc u la tin g t h e r m a l
c o n d u c tiv itie s:
A - a b s o lu te , d e r i v e d f r o m m e a s u r e d h e a t
i n p u t and g e o m e t r i c c o n s i d e r a t i o n s .
R - r e l a t i v e , d e r iv e d f r o m a c e ll c o n s ta n t
o b ta in ed f r o m a s ta n d a r d liq u id of
know n t h e r m a l co n d u c tiv ity .
12
geometrical configuration and mode of operation. All of
the steady-state devices, however, suffer from two major
problems which affect the ease of operation and the
reliability of the results.
The operation of a steady-state thermal conduc
tivity apparatus is a rather tedious procedure in that
6 to 14 hours are required in order to achieve a constant
temperature distribution from the heat source, through
the test liquid, to the heat sink. This preliminary
time period can be reduced by increasing the temperature
of the source relative to the sink, but only by risking
a severe penalty in reliability resulting from small
natural convection currents becoming established within
the test liquid. All thermal conductivity measurements
are plagued by this possibility of natural convection.
This phenomenon constitutes the single greatest source
of possible error. The problem is unfortunately com
pounded in steady-state devices by the fact that
existence of natural convection is rarely known at the
time measurements are being conducted. Natural convection
can only be detected in these devices by one of two
methods; either the calculated thermal conductivity values
derived from measured data are obviously too high, or by
the time consuming replication of results using a lower
heat flux from source to sink. It can thus be seen that
13
the two major problems affecting steady-state determina
tions undesirably reinforce one another; long durations
for the establishment of constant temperature distribu
tions, and the possibility of undetected natural
convection.
An appreciation of the problem of employing steady-
state devices for the measurement of thermal conductivity
can be gained by examining the history of reported results
on a single liquid. Liquid toluene has been investigated
by experimentalists more than any other organic liquid.
The experimental results are summarized in Table II-2.
In examining Table II-2, one must assume that the purity
of toluene was no factor in the generation of the data.
It is believed that the general decline in the magnitude
of the reported data with respect to the passing years
is a function of the greater appreciation of natural
convection which occurs undetected in these steady-state
devices. It is further felt that the leveling off of
this decline during the past decade reflects the essential
elimination of this problem. This is substantiated in
part by the careful experimental work of Ziebland (71)
in which the author proposed that toluene be used as a
thermal conductivity standard.
TABLE II-2
14
E x p e r i m e n t a l R e s u lt s
for the
T h e r m a l C o n d u c tiv ity of T o u le n e @ 20°C
Y e a r O b s e r v e r
E x p T . **
M eth o d
k 20°C
J / s e c . c m ° C
X 1 0 " 5
dk / dt
X 1 0 " 5
192 3 B’ r id g m a n CSA 154. 7 - 0 . 2 3 0
1924 R ic e CSR 141. 3 - 0 .4 3 5
1930 S m ith CSA 148. 7 - 0 . 1 7 6
1931 Shiba P I E Z O . 147. 0
_
1934 K a r d o s WSR 145. 0 -
1949 A b a s - Z ade WSA
139. 4 - 0 . 2 3 4
1951 R ie d e l CSA 136. 0 - 0 .2 5 5
1954 S c h m id t CSA 136. 1 - 0 .2 6 0
1956 C h a llo n e r P SA
137. 9 - 0 . 3 1 4
1956 F r o n t a s e v P SA 136. 5 -
1957 V a r g a f t ik WSA 134. 8
- 0 . 2 3 9
1957 B r ig g s CSR 136. 5 - 0 .0 7 1
1959 M c C r e a d y CSA 138. 8 - 0 .2 2 2
1959 F r o n t a s e v P S A 136. 1 -
1961 Zie bland CSA 134. 4 - 0 .2 8 5
1963 J a m i e son WSA 133. 9
-
1963 H o r r o c k s W TA 1 3 4 .6 - 0 . 2 92
1965 V e n a r t CSA
132. 9 - 0 .2 6 7
* D a ta ta k e n f r o m s u r v e y c o n d u c te d by J a m i e s o n (27)
** R e f e r to T a b le I I - 1 for an e x p la n a tio n of a b b re v .
N ote: To c o n v e r t k into c o n v e n tio n a l E n g l is h units of
B t u / h r ft ° F , m u ltip ly by 57. 8.
15
The problems associated with the employment of
steady-state thermal conductivity apparatus can be greatly
reduced by using a transient type of apparatus.
The employment of such an apparatus reduces the
preliminary time period to a minimum since static thermal
equilibrium is all that is required prior to data col
lection. The second problem, of natural convection, is
essentially eliminated if one can employ a transient
apparatus which detects natural convection at the same
time heat flux measurements are being recorded. With
the advent of fast responding electro-mechanical re
corders, these transient heat fluxes can now be measured
provided the heat generation within either the heat source,
or the sink, can be converted into electrical parameters.
The transient operation of a hot-wire apparatus satis
fies this provision since the temperature change within
such a source directly affects its electrical resistance.
Furthermore, the temperature rise of a thin, electrically
heated wire, suspended in a liquid, can be precisely
predicted by mathematical relationships derived from
Fourier's conduction law. Departure from this pre
dicted time-temperature relationship generally indicates
the presence of heat transfer from the hot-wire source
into the surrounding liquid sink by means other than
pure conduction. It can thus be seen that the transient
16
operation of a hot-wire apparatus can be used to generate
thermal conductivity data rapidly from which most un
certainties regarding convection have been eliminated.
For this reason, data reported by experimentalists employ
ing such a device are apt to be more reliable than data
generated from steady-state apparatus.
C. Choice of Liquids for Correlation Studies
The basic criterion for the choice of candidate
liquids was dictated by the desire to generate thermal
conductivity correlations applicable to polar as well as
non-polar liquids; attention was, therefore, mainly
directed toward liquids possessing high dip&le moments and
dielectric constants.
The required thermal conductivity data were obtained
from two distinct sources: the literature and first-hand
experimentation. The incorporation of literature values
was restricted, for the most part, to those experimental
ists employing some type of transient hot-wire apparatus.
These were:
Horrocks and McLaughlin 1960 (26)
Grassmann 1962 (19)
Jamieson 1963 (27)
Jobst 1964 (28)
The data of Riedel (52, 53), taken from two differ
ing steady-state apparatus, were also included because
17
these results are considered by most present-day investi
gators to be highly reliable. Data on 2-furaldehyde by
Schmidt (59) and on glycerol by Mason (36) were also in
corporated by virtue of their unique polar properties,
despite a lack of verification as to these authors'
reliability in the field of liquid thermal conductivities.
In addition to the above sources of literature
data, results for some of the non-polar liquids were
taken from Sakiadis and Coates merely for the sake of
completeness. (It should be noted that these data could
not always be correlated.)
First-hand experimental thermal conductivity data
were obtained for those liquids which showed interestingly
high polar properties and which were available from com-
merical distributors of reagent-grade chemicals. Experi
mental data were also obtained for a few non-polar liquids
of special interest.
Thermal conductivity data were thus compiled for
tne 56 liquids listed in Table 1-1, thermal conductivity
correlations are developed for all the chemical groups
listed except the carboxylic acids (.Nos. 43, 44, 45).
Reasons for this non-applicability are given in later
sections.
CHAPTER III
TRANSIENT HOT-WIRE APPARATUS AND THE COLLECTION OF
EXPERIMENTAL THERMAL CONDUCTIVITY DATA
A . Background
In view of the paucity of reliable thermal conduc
tivity data, especially for the less common, highly polar
liquids, it was considered necessary to collect new
experimental data. This was facilitated greatly by the
development of new, reliable and exceedingly fast apparatus
developed by P. Grassmann (18, 19). This was a comparative
apparatus of the transient hot-wire type and differed
greatly from most of the devices which were known
previously.
The concept for the transient hot-wire method for
the determination of thermal conductivity was first sug
gested by Staihane and Pyk in 1931 (61) . The method was
employed for liquids by van der Held and van Drunen in
1949 (22) and later by Gillam and Lamm in 1955 (17) , but
had not been fully exploited by these workers due to
difficulties in techniques. The first satisfactory ab
solute determination by a transient hot-wire apparatus was
19
conducted by Horrocks and McLaughlin in 1960 (26) . A far
simpler comparative method was then demonstrated by Grass-
mann in 1962 and it is a slightly modified copy of this
device which has been used for the collection of experi
mental data for this dissertation.
B. Description of Apparatus
In the transient operation of a hot-wire apparatus,
a constant electrical current is passed through a thin
wire which is suspended vertically within a liquid medium,
initially in thermal equilibrium with its surroundings.
As the wire temperature increases due to its electrical
resistance, it loses heat, by conduction, into the sur
rounding liquid. After a very brief induction period of
about 1/10 of a second, the heat transfer rate from the
wire source into the liquid becomes constant, provided
that:
1) the surrounding liquid is large enough
to absorb all the heat transferred and
still retain its initial equilibrium
temperature at some point removed from the
heat source;
2) the physical properties of the liquid do
not change appreciably due to the absorption
of the heat.
Both of these provisions are relatively easy to
meet since the duration of the transient operation is
about 4 to 10 seconds and the temperature increase in the
wire itself is about 2 to 6° F.
If the electrically heated wire is immersed in a
liquid of very low thermal conductivity, little heat will
be transferred from the wire source into the liquid sink.
The result is a rather rapid temperature rise within the
wire, which in turn can change the electrical resistance
of the wire depending upon the metal chosen. If the im
mersed wire is made to be one arm of a balanced Wheatstone
bridge, then its change of resistance with respect to
time can be measured as the voltage output of the un
balanced bridge circuit. The output voltage of the Wheat
stone bridge is directly proportional to the resistance
change of the heated wire, which, in turn, is an inverse
function of the thermal conductivity of the surrounding
1iquid.
Fourier's empirical heat conduction equation has
been solved for a cylindrical element of infinite length
with constant heat generation and surrounded by an in
finite homogeneous medium by Carslaw and Jaeger (11).
Using an initial boundary condition of constant tempera
ture, the temperature in the wire is described by:
21
where:
T = temperature rise of the wire
r = radius of the wire
0 = time
q^ = heat generated per unit time and per unit
1ength
a = thermal diffusivity of the liquid = -----
cpP
k - thermal conductivity of the liquid
Ei(-x) = the exponential integral.
At a fixed radial distance of r = R, the time
dependence of temperature can be obtained from the above
equation on expanding the exponential integral for small
2
values of (R /4a0):
T(R,0) = .qj : In 9 + In -4£L_ + — ft! ■ + ... - y
v 4rk r2 4a0 '
Eq. 111-1
where : y = 0.5772 is Euler’s constant.
The derivation and solution of Eq. III-l required a
number of simplifying assumptions. A careful study of
these assumptions, as well as experimental limitations,
has been conducted by Horrocks and McLaughlin (26). A
summary of these is to be found in Appendix A. The con
clusions were that the employment of Eq. III-l is valid
for all time periods with a maximum error of less than
0.011. If Eq. III-l is employed over a time span 0-^ to ©2
22
2
where 0^ > 0.1 sec., and furthermore, if R /4a0 is less
than 0.12 at 0^, then Eq. III-l can be reduced to the
following approximation:
T(R]_®2^ " TCR101: 1 = " T O T ln Ecl* 111-2
Eq.III-2 yields the thermal conductivity of a
liquid directly as a log function of time, thereby elim
inating the liquid's thermal diffusivity. A careful in
vestigation by Horrocks and McLaughlin led these authors
to conclude that for suitable intervals of 0-^ and &2>
Eq. 111 -2 will describe the temperature rise of a hot
wire to within M).l% (26). Any negative departure from
this log function could then be ascribed to increased heat
transfer from the heated wire element by natural convec
tion in the surrounding liquid. Positive temperature
deviations are rare and can be ascribed to a number of
trivial possibilities. Actual data taken by P. Grassmann
(19) on a number of fluids surrounding an electrically
heated wire are shown in Figure III-l. The departure from
linearity as time increases for some of the fluids, was
due to natural convection causing an increased rate of
heat transfer from the hot wire. The initial surges were
due to a combination of several factors:
a) momentary heat fluxes from the wire
as the circuit was closed;
TEM PERA TU RE RISE
23
O
o
L o g a rith m of T im e , s e c .
F IG U R E III-l
T E M P E R A T U R E RISE IN H O T -W IR E E L E M E N T VS. T IM E
b) non-applicability of Eq. 111-2 for short-
initial time periods where the series terms
of Eq. III-l have not sufficiently decayed;
c) inertial lag within the recorder used to
measure the voltage output as a function of
time and temperature of the heated wire.
If a hot-wire apparatus is used to generate
transient temperature data for the direct calculation of
liquid thermal conductivities, then the heat input para
meter of Eq. III-2 must be carefully measured as a
function of time. In the work of Horrocks and McLaughlin
(26), this painstaking procedure was carried out with a
reported precision of +0.25%. A far easier and much
faster approach was taken by Grassmann (19) where the
temperature response of a hot wire immersed in an unknown
fluid was compared to the response of another hot wire
immersed in a liquid of known thermal conductivity. A
simple circuit diagram for Grassmann's apparatus is shown
in Figure 111- 2. Such a plan has a twofold purpose.
First, a log function of time is generated on the X-axis
of the X-Y recorder by a Wheatstone bridge circuit iden
tical to that of the unknown Y circuit. This results
directly in a straight line plot on the X-Y recorder
since both voltage inputs are now identical logarithmic
25
X -Y
R E C O R D E R
G A L V O .
C IR C U IT C IR C U IT
R -3 R -3
R -2
UNKOW N
LIQUID
/ R E F .
f LIQUID
u s e d a s log
g e n e r a t o r )
MV
P O W E R B A L A N C E
F IG U R E III-2
T R A N S IE N T H O T -W IR E T H E R M A L C O N D U C T IV IT Y A P P A R A T U S
26
functions of time, provided natural convection does not
occur within either liquid. (For this reason, the X cell,
which merely drives the X-axis of the recorder, is filled
with a highly viscous fluid and is maintained in a constant
environment for the duration of all experimental work.)
The second purpose of Grassmann*s plan was that the pains
taking collection of data for the evaluation of Eq. 111 -2
could be eliminated entirely if a cell constant could be
obtained for the Wheatstone bridge response of the Y
circuit. This could be accomplished by measuring the
resulting slope on the X-Y recorder when an equal current
of suitable strength were passed through both Wheatstone
bridge circuits of Figure III-2, provided the Y cell were
filled with a liquid of known thermal conductivity. The
product of the known thermal conductivity of the calibra
tion liquid and the resulting slope on the recorder
constitutes the cell constant for the Y cell, provided
nothing is changed in the entire apparatus. The thermal
conductivity of any new liquid in the Y cell is then
proportional to the cell constant in the following manner:
k.
cell constant
or,
unknown slope with unknown liq.
k
unknown
^calib. liq-) (slope with calib. liq.)
slope with unknown liq.
27
The liquid used for calibration was reagent grade
toluene obtained from both Mallinckrodt Chemical Co. and
Allied Chemical Co. Further purification was not per
formed. The thermal conductivity data used for toluene
were those reported in 1961 by H. Ziebland (71). This
author recommended a weighted least-square equation to
serve as a liquid thermal conductivity standard. Zieb
land1 s equation incorporates his own data as well as the
results from a few other authors. In 1966, the National
Bureau of Standards (49) also proposed that toluene be
used as a thermal conductivity standard. The N.B.S.
equation, however, incorporates data from too many
sources; some of which are questioned. Therefore, both
for the sake of convenience and because it is felt that
Ziebland1s own data represent the most accurate deter
mination, a least-square fit through Ziebland^ data
has been taken as the sole reference for the calibration
of the apparatus (refer to Figure A-4, page 102, for
the data on toluene which are cited above).
The experimental thermal conductivity data were
obtained from four pressurized cells in conjunction with
the constant X cell. Data were recorded over a transient
heating period of less than 10 seconds. Ten repetitive
measurements were taken at 1-minute intervals in order to
establish an average value and a 951 confidence limit on
28
each data point. About 10 or 12 data points were taken
at differing temperatures on each liquid sample and there
were usually at least two samples for each liquid
measured. During an 8-hour period, 20 data points could
be obtained on four liquid samples at five temperature
levels ranging from 60 to 250° F.
A detailed circuit diagram of this apparatus can
be found in Appendix A along with operating notes, tech
nical specifications and examples of actual raw data.
C. Proof of Apparatus and Collection of Data
The transient hot-wire apparatus described in the
previous section was at various times equipped with
different hot-wire elements. Each element has a dif
ferent coefficient of thermal resistance and therefore
required different power levels for optimum operation.
There appeared to be, however, little difference in the
precision of results obtained from the following elements:
Invar
Platinum
Platinum--10% Iridium
Platinum--20% Iridium
Iridium
Because of the superior tensile strength of the
last two materials, all the experimental data were col
lected using these hot-wire elements.
29
Proof of the reliability of the apparatus was ob
tained by measuring the thermal conductivity of n-hexane
and ethanol and comparing the results with those obtained
by Grassmann (19), Jobst (28) and Riedel (53). In all
cases, the experimental data agreed with the values
reported by these authors to within +2% in the range of
70 to 180° F (refer to Appendix B for actual comparisons).
Experimental data were collected on a total of
23 liquids of which four were non-polar, 13 were polar,
and six were complex hydrocarbons of unknown composition.
These latter liquids, as well as five of the polar
species could not be incorporated into the correlations
due to a lack of necessary parametric data. The actual
data on all of these liquids are given in Appendix B.
A summary of these results is given in Table III-l.
The precision of the data obtained from this
apparatus ranged from about 0.5 to 2%. The accuracy of
the data is relative to the toluene calibration data of
Ziebland (71) . The range in precision appears to be
dependent upon the viscosity of the liquid and its
effect upon the onset of natural convection. As the
apparatus exists today (with either a Platinum--20%
Iridium or a pure Iridium hot-wire element), there are
three limitations which should be noted:
TABLE III-l
30
S u m m a r y of E x p e r i m e n t a l R e s u lt s
a t 100 p s ig
# L iq u id
T h e r m a l
C onduct.
B tu
dk / dt
X 1 0 -5
B tu
N u m b e r
of D a ta
P o in ts
T e m p .
R a n g e
° F
P e r c e n t
P r e c i s i o n
in
D ata h r ft ° F
@ 7 7 °F
h r ft ° F 2
@ 7 7 °F
3 n -H e x a n e 0 .0 6 7 8 0 - 1 9 . 2 6 18 73 -2 0 0 1.51
8 M e th y lc y c lo -
h ex an e 0. 06421 - 7. 71 21 8 2 -2 4 7 1. 15
9 n - H e p ta n e 0 .0 7 1 1 6 - 8. 42
19 78 -1 8 6 1. 40
12 n - D e c a n e 0. 07716 - 1 1 .2 0 24
8 4 -2 4 9 1. 20
18 C y c lo h e x a n o l 0. 07748 - 3 .9 8 * 23 7 7 -2 2 8 0. 75
28 P r o p y le n e gycol 0. 11590
- 0. 69 39 64 -2 0 9 1. 09
30 2 - N itr o p r o p a n e 0 .0 7 8 7 8 - 9. 54 16 8 1 -2 3 3 1. 56
31 N itro b e n z e n e 0 .0 8 5 4 3 - 7. 10 22 8 0 -2 4 4 1. 00
32 m - N i t r o toluene 0 .0 8 0 4 7 - 5 .9 9 26 8 0 -2 4 9 1. 10
33 B e n z o n tr ile 0 .0 8 6 0 8 - 8. 06 21
7 7 -2 2 9 1. 60
34 C a r b o n t e t r a -
c h lo rid e 0 .0 5 8 0 3 - 7. 66 15 7 7 -1 9 6 0. 90
42 T e t r a c h l o r oeth-
ylene 0 .0 6 2 2 2 - 6. 69 12 7 7 .1 6 6 1. 80
46 1, 3 - B u ta n e d io l 0 .1 0 6 7 5 - 1 3 .5 6 30 6 4 -2 1 5 1. 90
47 1, 4- B u ta n e d io l 0 .1 2 2 3 7 - 8. 37 28 6 3 -2 1 5 1. 70
48 N, N - D i m e t h y l -
f o r m a m i d e I n c o n s is te n t data; se e A p p e n d ix B -3
49 N, N - D i m e t h l -
a c e t a m i d e 0 .0 9 6 4 3 - 1 3 .0 6 21 7 6 -2 4 4
1. 89
50 N - M e th y l -
a c e t a m i d e R e s u l t s doubtful; low e l e c t r i cal r e s i s t a n c e
51 D u P o n t O il 0 .0 8 4 2 2 - 4 .3 2 * * 26 8 0-248 0. 60
52 Gulf H a r m o n y
#204 0 .0 9 1 8 8 - 4. 01 12 90-248 0. 44
53 C h e v ro n A lta
V is #530 0. 06674 - 0. 24 16 75-250 0. 41
54 Gulf O il #896 0 .0 7 7 8 0 - 6. 03 15 86-249 0. 68
55 Shell P r e m ,
Die s e lin e 0 .0 7 2 1 8 - 6 .2 0 22 7 8 -2 5 0 0. 78
56 C h e v ro n D ie s e l
F uel 0 .0 7 2 0 3 - 5. 43 6 9 0 -2 4 6 0. 35
D a ta not lin e a r ab o v e 1 5 0 ° F
** D a ta not lin e a r above 2 1 0 ° F
Si
1. Only liquids of high electrical resistance
can be measured. The electrical resistance
of a liquid must exceed 15,000 ohms per
inch.
2. The operating range of the apparatus is
60 to 250° F at a maximum pressure of
500 psig.
3. Liquids of low viscosity and high coefficients
of thermal expansion, such as n-pentane,
cannot be measured above 160° F.
It should be noted that all experimental data were
collected at a cell pressure of 100 psig. Comparisons
were made with data collected at 0 psig for some liquids
and no discernible differences were detected.
CHAPTER IV
PREDICTION FOR THE THERMAL CONDUCTIVITY OF
LIQUIDS AT 77° F
A. Existing Correlations of k vs. T
Predictions for the thermal conductivity of
liquids have been derived by many investigators along both
theoretical and empirical lines. The theoretical approach
has been severely handicapped, however, by the lack of
sufficient information about liquid structures and such
basic necessities as molecular shape, inter-molecular
distance and inter-molecular forces and vibrations. In
vestigators along the theoretical line have been forced
to develop several differing idealized liquid systems
in which the necessary parameters could be approximated.
The results of these approximations could then be trans
ferred to only the simplest of liquids such as argon,
methane and carbon tetrachloride. From a theoretician's
viewpoint (38), great progress has been made in this
direction. From a practical standpoint, however, even
the best recognized of these expressions (43) yield
results for simple liquids which are between 5 and 60% in
33
error (24) . A comprehensive review of theoretical models
and derivations for the prediction of liquid thermal con
ductivities has been written by McLaughlin (38).
Predictions for liquid thermal conductivity based
on empirical or semi - empirical considerations have been
somewhat more successful than those based on purely
theoretical grounds. Even in this class, however, many of
the published predictions are in error by 15 to 30%. In
the first edition of Reid and Sherwood's "The Properties
of Gases and Liquids" published in 1958 (50), the authors
closely reviewed eight methods for predicting liquid
thermal conductivities (6, 10, 29, 49, 56, 57, 60), and
in the authors' own words, "None is reliable. ..."
A secondary problem which plagued the investigators
of a decade ago was the fact that liquid thermal conduc
tivities were rather difficult to measure precisely.
Literature values for many of the more common liquids
often differed by as much as 20%. Values for the less
common, highly polar liquids often were reported 50% apart
with even negative and positive temperature dependencies
reported for the same liquid (27). It is not surprising,
therefore, that many of the investigators who developed
empirical predictions, relied primarily upon their
own experimental data. Since thermal conductivity
versus temperature data used to require an inordinate
amount of time, few investigators prior to 1955 were able
to publish a comprehensive quantity of data. However,
since the extensive publications of Sakiadis and Coates in
1955 and 1957 (56, 57), most authors of empirical predic
tions have relied upon these works as reference material.
Unfortunately, the values of Sakiadis and Coates are
often from 5 to 101 higher than data reported by several
other highly respected experimentalists (18, 26, 28, 52).
The weight of evidence to date tends to substantiate the
belief that the lower thermal conductivity values are
more nearly correct than the data of Sakiadis and Coates.
In 1962, Robbins and Kingrea (54) published an
empirical method for the prediction of liquid thermal
conductivities relying heavily upon the experimental data
of Sakiadis and Coates. This correlation is by far the
best method to be published to date. As testimony to
this, the second edition of Reid and Sherwood's book
"The Properties of Gases and Liquids" (51) recommends
the estimation of Robbins and Kingrea as the only work
to be considered for both polar as well as non-polar
liquids. Robbins and Kingrea predicted 142 values of
thermal conductivity at various temperatures from 68 to
over 200° F for 70 liquids with an average deviation from
experimental data of less than 4%. Even when more
reliable data are used as reference material, the Robbins
and Kingrea correlation still yields an average deviation
of less than 6% .
B . The Robbins and Kingrea Estimation for Liquid Thermal
Conductivity vs. Temperature
Robbins and Kingrea used as a foundation for their
work the following empirical relationship for thermal
conductivity first proposed by Weber in 1880 (54):
1/3
k = 0.00347p C
P
M
Eq. IV-1
where
k = thermal conductivity, Btu/hr ft ° F
0^ = heat capacity, Btu/lb ° F
p = * density, lb/ft"^
M = molecular weight
The Weber equation as written has two major limita
tions; it shows little temperature dependency for any
liquid and does not adequately predict the thermal con
ductivity of associated liquids. These liquids are known
to have considerable hydrogen bonding between molecules
(41, 45). It is generally accepted that a liquid's entropy
of vaporization at the normal boiling point is an indica
tion of the degree of hydrogen bonding. This has been
derived from Trouton's (66) observation that the entropy
of vaporization tended to have a constant value of
21 Btu/lb mole 0 R for non-polar liquids while the value
36
for associated liquids was generally higher. Several in
vestigators in the field of liquid thermal conductivities
(44, 67) have modified Weber’s basic equation to include
the entropy ratio term of AS /21 to account for a
vap
liquid's degree of association. Trouton's constant, how
ever, tends to drift to higher values as liquids with
higher normal boiling points are investigated. To remedy
this, several attempts (3, 14, 21, 23, 47) have been made
to modify Trouton's constant. Robbins and Kingrea chose
the work of Everett (15) as a more reliable estimator of
a liquid's degree of association and modified Weber's
equation by introducing the entropy ratio AS*/19.7 on
the right side of the Eq. IV-1. An explanation of
Everett's derivation for AS* can be found in Chapter VI.
Robbins and Kingrea further modified Weber's
equation to predict more accurately a liquid's tempera
ture dependency by multiplying the right side of Eq. IV-1
by (T /T)^ and changing the constant. T is the liquid's
c c
critical temperature in degrees Rankine. Robbins and
Kingrea empirically set the exponent N equal to 1 for
organic liquids lighter than water and equal to 0 for
liquids more dense than water.
One further modification of the basic Weber equa
tion was made by Robbins and Kingrea. These authors
included a molecular structure "H in drance Factor" into
37
their correlation. This hindrance factor, H, ranged from
-1 to +5 depending upon the functional group attached to
the basic, straight-chain, hydrocarbon molecule. The
final relationship of Robbins and Kingrea, after com
bining the several modifications to the basic Weber
Equation was published as:
, _ (86.0 - 4.83H)
K 1000 AS*
T
0. 55 1
Tc
N
P cp
P
M
1/3
where:
k = thermal conductivity, Btu/hr ft ° F
H = structural hindrance factor, dimensionless
AS* = Everett’s entropy of vaporization, Btu/lb mole°R
T = temperature, ° R at which evaluation is made
Tc = critical temperature, ° R
N = temperature dependency factor:
3
1 for organic liquids less than 62 lb/ft
3
0 for organic liquids more than 62 lb/ft
3
p = density at temperature T, lb/ft
Cp = heat capacity at temperature T, Btu/lb ° F
M = molecular weight
The Robbins and Kingrea correlation as written
above, while providing a relatively accurate prediction
of liquid thermal conductivities over a useful tempera
ture range, does have some drawbacks and limitations
which can be overcome. The limitations are twofold:
38
1. Thermal conductivities of inorganic
liquids are not adequately predicted.
2. Considerable physical data were required
and furthermore, heat capacity and density
had to be evaluated at each temperature
for which predictions for k were to be made.
There are, furthermore, inherent drawbacks in the
use of empirical constants derived from structural con
siderations. The authors list, in their work (54),
25 hindrance factors and suggest an additive technique
when more than one functional group is included in any
liquid. Experience (51) has shown this to be unreliable
for many correlations and the failure of this correlation
to predict the correct thermal conductivity of glycerine,
carbontetrachloride and furfural are examples. A further
drawback is the arbitrary use of the temperature
dependency factor, N. It has been found (51) that some
dense liquids are better described by the Robbins and
Kingrea correlation if the exponent N were set equal to
one rather than zero, and the converse is true for
several liquids lighter than water.
It is the purpose of this dissertation to develop
a general thermal conductivity correlation which, in
accuracy, is equal to or better than the Robbins and
39
Kingrea estimation and, furthermore, will include the
following advantages:
1. No arbitrary constants; reliance will be
placed exclusively upon physical properties
which are easier to obtain from the
literature than thermal conductivity itself.
2. The evaluation of all physical constants
will be restricted to only one standard
temperature, either 77° F [25° C) or the normal
boiling point where the entropy of vaporization
is involved.
In the development of the Robbins and Kingrea
correlation, the authors pointed out that for the non
polar, straight-chained hydrocarbons, the basic Weber
, Tc
Eq. IV-1, when modified by the temperature term
1
9
T
was an adequate prediction of the thermal conductivities
of these paraffinic liquids. The authors also changed
Weber's proportionality constant to conform to the modern
experimental data of their day. The following equation
represents the Robbins and Kingrea modification of the
basic Weber Equation for the prediction of the thermal
conductivity of paraffinic liquids over a temperature
range extending from 68° F to 170° F:
1/3
k = 0.00240
f T ]
r
n r
f
p
. T .
p tp
I M
Eq. IV-2
40
The improved correlation for liquid thermal con
ductivities which will be presented in this dissertation
is based upon the above modification of the Weber
Equation.
C. The Modified Weber Equation for the Prediction of the
Thermal Conductivity of Non-Polar Liquids at 77°~F
The basis for the prediction of liquid thermal
conductivities at 11° F will be the previously derived
Eq. IV-2. It has now been found, that when this equation
is limited to an ambient temperature, it also predicts
accurate values for many other non-polar liquids, regard
less of molecular structure. When the 13 non-polar
liquids in the beginning of Table 1-1 were checked
against this equation, it was found that the more modern
data available at the present time dictate a slight
change in Robbins and Kingrea's proportionality constant:
Tc
k = 0 .00230 p C
T P
P
M
1/3
Since predictions employing the above equation
will only be required at 77° F (534° R) , the expression
can be simplified to:
T ( _ i1/3
k7y 0.00433 100Q p Cp
M
Eq. IV-3
Equation IV-3 will now be used for predicting the
thermal conductivity of non-polar liquids at 11° F, and
will be used as a basis for the prediction of polar
41
liquids as well. Table IV-1 shows the agreement between
predicted and experimental values for the 13 non-polar
liquids of Table 1-1. It should be noted that for the
sake of completeness, reliance was placed on some of the
data published by Sakiadis and Coates. One further note
concerning Table IV-1 is in order; the large discrepancy
for methylcyclohexane (No. 8) is believed to be due to
heat capacity and/or critical temperature data (refer
to Appendix D for data and source). This belief is
justified by the very close agreement obtained between
the experimental thermal conductivity values for this
liquid and the prediction of Horrocks and McLaughlin
for the temperature dependency which relies exclusively
upon density and temperature data. While this question
will be discussed more fully in the following chapter,
the argument is put forth at this time to reinforce the
contention that the experimental thermal conductivity
data for methylcyclohexane are correct and that Eq. IV-3
is a valid representation of the thermal conductivity of
non-polar liquids.
D. Correlation for the Deviation of Polar Liquids from
the Predictions of the Modified Weber Equation
at 776 F
When Eq. IV-3, as derived in the previous section,
is used to predict the thermal conductivity of polar
liquids, the predictions are invariably higher than the
TABLE IV-1
42
E x p e r i m e n t a l and P r e d i c t e d T h e r m a l C o n d u c tiv itie s
fo r the N o n - P o l a r L iq u id s a t 7 7 ° F
# L iquid
^■predict
E q . I V - 3 *
k e x p t'l.
B t u / h r ft ° F R e f e r e n c e
A k
E q - E x p
%
Diff.
1 n - P e n t a n e 0. 06577 0 .0 6 5 8 3 R ie d e l - .0 0 0 0 6 -0 . 1
2 C y c lo -
p e n ta n e 0 .0 6 9 1 0 0 .0 7 5 3 1 S ak ia d is -.0 0 6 2 1 -8 . 3
3 n -H e x a n e 0.06751 0. 06823 M alian -.0 0 0 7 2 - 1 . 0
4 C y c lo -
hexane 0. 06975 0 .0 6 8 9 0 H o r r o c k s . .0 0 0 8 5 1.2
5 2 - M e th y l-
p en tan e 0. 06484 0 .0 6 4 5 0 S ak ia d is .0 0 0 3 4 0. 5
6 2, 3 -D im d h -
ylbutane 0. 06450 0. 06023 S a k ia d is .0 0 4 2 7 7. 1
7 M e th y lc y -
c lo p e n ta n e 0. 07048 0 .0 6 8 8 8 S ak ia d is .0 0 1 6 0 2. 3
8 M e th y lc y
c lo h e x a n e 0. 07345 0. 06421 M alian .0 0 9 2 4 14. 4
9 n - H e p ta n e 0 .0 7 0 5 0 0 .0 7 1 1 6 M alia n - .0 0 0 6 6 -0. 9
10 n - O c ta n e 0 .0 7 2 8 4 0 .0 7 3 5 2 F illip p o v - .0 0 0 6 8
i
o
11 n -N o n a n e 0. 07540 0 .0 8 0 6 9 S ak ia d is - .0 0 5 2 9 - 6 . 5
12 n - D e c a n e 0. 07784 0. 07716 M alian .00068 0. 9
13 B e n z e n e 0 .0 8 5 8 9 0 .0 8 4 3 9 R ie d e l .0 0 1 5 0 1 .8
T 1/3
* E q . IV -3; k 77 = 0 .0 0 4 3 3 -9__ p C p ( J U B t u / h r ft ° F
' 1000 M
corresponding experimental data. This is shown in
Table IV-2 where these comparisons are made for all the
polar liquids listed initially in Table 1-1 for which the
necessary physical parametric properties are available.
It should come as no surprise that Eq. IV-3 predicts such
large deviations for the polar liquids. Many of these
polar liquids are composed of associated molecules which
are held together by weak, intermolecular hydrogen bonds.
Several investigators (9, 44, 54, 60) have attempted to
modify existing thermal conductivity relationships to
describe both polar as well as non-polar liquids by the
use of a suitable associative parameter. These in
vestigators have all used some form of-the entropy of
vaporization of a liquid at its normal boiling point as
a measure of the degree of intermolecular association.
The use of some form of this term, however, is not a
panacea for all deviations of polar liquids. This may
be due to the fact that while all associated liquids are
polar, not all polar liquids are associated (41) . It is
suggested that a combination of a liquid's polar and
associative properties should be used in any attempt to
correlate a polar liquid’s deviation from previously
derived non-polar relationships. The types of deviation
which were listed for the polar liquids in Table IV-2
further suggest that an additive correction term composed
TABLE IV-2 44
D e v ia tio n s of P o l a r L iq u id s f r o m the P r e d i c t i o n s
of th e M odified W e b e r E q u a tio n IV -3 a t 7 7 ° F
k-expt'l D e v ia tio n
p r e d i c t B tu / R e f e r
A k %
#
L iquid E q. IV -3 h r . ft. ° F en ce Eq*rExp. Diff.
14 M e th an o l 0 .1 3 3 4 0 0 .1 0 6 4 0 J o b s t .0 2 7 0 0 25. 4
15 E th a n o l 0. 1 1825 0 .0 9 4 0 0 J o b s t .0 2 4 2 5 25. 8
16 n - P r o p a n o l 0. 11184 0. 08645 J o b s t .0 2 5 3 9 29. 4
17 n - B u ta n o l 0 .1 1007 0 .0 8 8 1 9 R ie d e l .0 2 1 8 8 24. 8
18 C y c lo h e x a n o l 0. 11136 0. 07748 M alian .0 3 3 8 8 43. 7
19 A c e ta ld e h y d e 0 .1 0 9 8 9 0 .0 9 9 0 0 J o b s t .0 1 0 8 9
11. 0
20 n - P r o p i o n a l d e -
hyde 0. 09250 J o b s t
21 n - B u t y r ald e h y d e 0. 08403 J o b s t
22 F u r f u r a l 0. 1 5 9 H 0. 09271 S c h m id t .0 6 6 4 0 71. 6
23 A c e to n e 0. 09786 0. 09021 R ie d e l .0 0 5 7 3 6. 2
24 M e th y l- E th y l-
K etone 0. 10076 0. 08289 J o b s t .0 1 7 8 7 21. 6
25 W a te r 0 .4 7 4 0 2 0 .3 5 1 0 P o w e ll .1 2 302 35. 0
26 H e a v y W ater 0. 52747 0. 3405 V e n a r t .1 8 6 9 7 54. 9
27 E th y le n e g ly c o l (0. 21726)* 0. 14720 C fl ’ assm err .0 7 0 0 6 47. 6
28 P r o p y l e n e glycol (0. 18442)* 0. 11590 M alia n .0 6 8 5 2 59. 1
29 G ly c e r ol
(0. 25117)* 0 .1 7 0 0 0 M a s o n .081 17 47. 7
30
2 - N itr o p r o p a n e 0. 07878 M a lia n
31 N itr o b e n z e n e 0 .1 2 6 3 8 0 .0 8 5 4 3 M a lia n .0 4 0 9 5 47. 9
32 m - N it r o to lu e n e
0 .0 8 0 4 7 M a lia n
33 B e n z o n itr ile
0 .1 2 6 9 1 0 .0 8 6 0 8 M a lia n .0 4 0 8 3 42. 4
34
C a r b o n t e t r a c h l o -
r id e 0 .0 7 6 4 4 0 .0 5 8 0 3 M a lia n .01841 3 1 .7
35 C h l o r o f o r m 0 .0 8 2 4 1 0. 06826 Jamieson .0 1 4 1 5 20. 7
36
Io d o b en ze n e 0 .0 9 7 5 0 0. 05820 R ie d e l .0 3 9 3 0 67. 5
37 B r o m o b e n z e n e
0 .0 9 0 0 9 0. 06404 R ie d e l .0 2 6 0 5 40. 7
38
E th y lio d id e
0. 08359 0. 05156
R ie d e l .0 3 2 0 3 62. 1
39 E t h y lb r o m i d e 0. 07087 0. 05953 R ie d e l .0 1 1 3 4 19. 0
40 1, 2 - D ic h lo r o -
41
eth a n e
0 .0 9 7 9 7 0. 07728
R ie d e l
.0 2 0 6 9 26. 8
T r i c h l o r o -
eth y len e
0 .0 8 8 8 8
0. 06693 R ie d e l
.0 2 2 4 5 33. 8
42 T e t r a c h l o r o -
43
eth y le n e
0.08901
0. 06204
M a lia n .0 2 6 9 7 43. 5
F o r m i c A cid
0.1 6 3 8
0. 1286 J o b s t . 0352
21. 5
44 A c e tic A cid
0. 1371 0. 09242 J o b s t . 0447 32. 6
45 n - B u t y r i c A c id 0. 1 4 0 f
0. 08011 J o b s t . 0640
- 4 5 ,7
* k v a lu e s w e r e p r e d i c t e d by e m p lo y in g e s t i m a t e d c r i t i c a l
t e m p e r a t u r e s (Ref. 51)
45
of polar and associative properties could be affixed to
the non-polar Eq. IV-3 to make this expression general for
all liquids. The search for such an additive correlating
group was centered around the following physical
properties: (A discussion of these properties is given
in Chapter VI.)
1. Entropy of vaporization at the normal
boiling point, AS vap; or more precisely,
Everett's entropy of vaporization ratio
AS*/19-7, where AS* = 19.7 ± 0.7 Btu/lb mole °F
for 70 non-polar hydrocarbons.
2. Dipole moment, y, in electrostatic units.
3. Dielectric constant, e, evaluated at 77° F.
The search for a successful grouping of the above
parameters was essentially a trial-and-error process in
which a particular correlating group was compared with
the deviations of the thermal conductivity of the polar
liquids listed in Table IV-2 (excluding the carboxylic
acids, Nos. 43, 44, 45). The correlation study was
initially conducted without the nine halogenated hydro
carbons of Tables 1-1 and IV-2 (Nos. 34-42). As the
study was expanded to encompass these dense liquids, it
was found necessary to include a density ratio term
p/pu _ which tended to raise the value of the correlating
m2u
group for these liquids while lowering the value for the
46
remaining lighter fluids. A summary of the trial-and-
error process involving 32 permutations of the above
parameters is given in Appendix E. These permutations of
the correlating group, which is called $ , were tested
as a function of the thermal conductivity deviation Ak.
The best permutation tested had the form of:
AS*
f \
p
19.7
V
^ ph 9(v
This expression is plotted as a function of Ak in
Figure IV-1. A least square regression analysis of the
data indicates the following relationship:
Ak7?0F - (1.06 + 0.88$ ) x 10"3 Btu/hr ft °F
For non-polar liquids, the correlation group $,
has a nearly constant value of 2. For this reason, and
for the additional sake of simplicity, the Ak intercept
in the above expression has been eliminated so that the
thermal conductivity deviation of all liquids from the
modified Weber Equation IV-3 can be expressed as:
Ak?7o F = 0.00088$ Btu/hr ft ° F
The above expression can now be combined with Eq. IV-3 to
yield a general expression for the prediction of liquid
thermal conductivities at 7 7° F such that:
4 7
183 12C
• 25
•22
• 31
•38
• 33
20
25 100
125 50
A k x 1CT B t u /h r ft ° F
k - k
'm o d . W e b e r Eq. e x p t'l.
F IG U R E IV-1
C O R R E L A T IO N fo r th e D E V IA T IO N of P O L A R LIQUIDS f r o m
the P R E D I C T E D k V A L U E S of the M O D IF IE D W E B E R EQ ., 7 7 ° F
k?7o F = 0.00433
T O W
-P C,
M
48
1/3
0. 00088$
Eq. IV-4
where:
AS*
197T
h2o
(y + e)
The values of the parameters making up the cor
relating group $ can be found in Appendix D. The values
of the correlating group itself are given in Appendix C,
column 12. The calculated results of Eq. IV-4 are also
given in Appendix C, column 4 and are summarized in the
following Table IV-3.
Table IV-3 contains predicted thermal conductivity
values for 41 of the polar and non-polar liquids initially
listed in Table 1-1 for which parametric data are avail
able. Excluding the three carboxylic acids, relatively
accurate predictions were made for 31 of the 38 fluids.
The average deviation of these 31 liquids is ±3.31. It
should be noted that for ethylene glycol (No. 27),
propylene glycol (No. 28) and glycerol (No. 29), the
required critical temperature data were estimated using
the correlation of Lyderson as published in the reference
work of Reid and Sherwood (51) . The predicted thermal
conductivity values for the remaining seven liquids,
Nos, 8, 26, 34, 36, 39, and 42, deviated considerably
TABLE IV-3
49
P r e d i c t i o n fo r the T h e r m a l C o n d u c tiv ity of L iq u id s a t 7 7 ° F
by E q u a tio n IV -4
#
k ,
p r e d .
E q . IV -4
^ e x p t'l.
B t u / h r ft ° F
%
Diff.
#
k ,
p r e d .
E q . IV -4
^ e x p t'l.
B t u / h r ft ° F
%
Diff
1 0 .0 6 4 6 8 0. 06515 - 1. 7 23 0. 08299 0. 09213 - 9 . 9
2 0 .0 6 8 6 9 0. 07531 - 8 . 8 24 0. 08069 0. 08289 - 2 . 7
3 0 .0 6 7 5 2 0. 06823 - 1. 0 25 0. 3526 0. 3510 0. 5
4 0. 06962 0. 06890 1. o 26 0. 3925 0. 3405 15. 0
5 0 .0 6 4 7 3 0. 06450 0. 4 27 0. 15 320* 0. 14720 4. 1*
6 0 .0 6 4 3 4 0. 06023 6. 8 28 0. 12475* 0. 11590 7. 6*
7 0 .0 7 0 3 0 0. 06888 2. 0 29 0. 15921* 0. 17065 - 6. 7*
8 0 .0 7 2 3 5 0. 06421 13. 0 30 - 0. 07878 -
9 0 .0 7 0 5 2 0. 07116 - 0. 9 31 0. 08079 0. 08543 - 5 . 4
10 0 .0 7 2 8 0 0. 07352 - 1 . 0 32 - 0. 08047
-
11 0 .0 7 4 8 5 0. 08069 - 7. 2 33 0. 09257 0. 08608 7. 6
12 0 .0 7 7 7 4 0. 07716 0. 8 34 0. 07121 0. 05803 23
13 0 .0 8 5 0 6 0. 08439 0. 8 35 0. 06853 0. 06826 0. 4
14 0 .1 0 4 4 4 0. 10640 - 1. 8 36 0. 07860 0. 05820 36
15 0 .09361 0. 09400 - 0. 4 37 0. 07402 0. 06404 16
16 0 .0 8 8 5 2 0. 08645 2. 4 38 0. 04998 0. 05156 3. 1
17 0 .0 9 0 0 1 0. 08819 2. 1 39
0. 04819 0. 05953 -19
18 0 .0 7 4 4 9 0. 07748 - 3. 9 40 0. 07826 0. 0772 1 .3
19 0 .0 9 6 7 8 0. 09900 - 2 .2 41 0. 07175 0. 06645 8. 0
20 - 0. 09250 - 42 0. 08310 0. 06222 34
21 - 0. 08403 - 43 0. 13110 0. 1286
1 .9
22 0 .0 9 2 4 3 0. 09271 - 0. 2 44 0. 13188 0. 09242 29. 9
45 0. 13630 0. 0801 1 41. 2
* k v a lu e s w e r e p r e d i c t e d by e m p lo y in g e s t i m a t e d c r i t i c a l
t e m p e r a t u r e s (Ref. 51)
50
from the experimental results. A tentative explanation
has previously been presented for the deviation of the
non-polar liquid methylcyclohexane (No. 8); however,
explanations regarding the remaining six liquids are not
forthcoming at this time. Mention is again made of the
three carboxylic acids (Nos. 43, 44, 45) for which no
permutation of the additive correlating group 4 was
successful.
While the present grouping of additive parameters,
as arranged in Eq. IV-4 is not a universal predictor of
liquid thermal conductivities, it is, nevertheless, rela
tively accurate for most liquids, and, furthermore, is
free from arbitrary empirical constants. The following
chapter will show that a somewhat different permutation
of these same polar and associative properties, con
stitutes an excellent correlation for the temperature
dependency of thermal conductivity.
CHAPTER V
PREDICTION FOR THE TEMPERATURE DEPENDENCY OF
THERMAL CONDUCTIVITY AT 7 7° F
The prediction of the temperature dependency of
the thermal conductivity of liquids at 77° F is perhaps the
most significant feature of this dissertation. The im
portance of this statement is substantiated by the follow
ing:
1. With the exception of water and heavy
water, the thermal conductivities of all
the 56 liquids listed in Table 1-1 were
linear functions of temperature, at least
between the limits of 70 to 150° F. In all
but one case, this linearity held through
out the entire range of reported values,
usually well beyond 200° F. (In the
one case of cyclohexanol (No. 18), this
linearity ceased around 150° F). If
the temperature dependency of thermal con
ductivity were accurately known at 7 7° F,
51
then the thermal conductivities of most
liquids can be predicted up to a tempera
ture of 200 to 250° F.
2. The accuracy of the predicted temperature
dependency is such that when experimental
k data at 77° F were used as a reference
point, an average error of +2.2%, over a
temperature range extending to 200° F, is
obtained for the predicted thermal conduc
tivities of 36 out of the possible 45 pure
liquids appearing in Table 1-1 for which
parametric data are available. Of the
9 remaining pure liquids in Table 1-1,
experimental data on 4 were not avail
able above ambient temperature and the
3 carboxylic acids could not be cor
related. The last 2 uncorrelated liquids
are water and heavy water for which unique
values of temperature dependency do not
exist between the limits of 77 and 250° F.
The method by which the above accuracies in tem
perature dependency were obtained is based on the
theoretical work of Horrocks and McLaughlin (25). Their
relationship appears to be valid for most non-polar
liquids and for some complex hydrocarbon mixtures as well.
53
Furthermore, their relationship is relatively simple
in that a knowledge of a liquid's density change with
respect to temperature is all that is required in order
to calculate the liquid's temperature dependency of
thermal conductivity. Most polar liquids have been
found to deviate markedly from the simple Horrocks-
McLaughlin relationship. A method has been found and
is presented in this paper, however, which can accurately
account for this deviation.
A. The Horrocks-McLaughlin Relationship
The temperature dependency relationship proposed
by Horrocks and McLaughlin (25) is derived from a vibra
tional theory of thermal conductivity in which it is
assumed that liquid molecules are held in a quasi-lattice
structure. Excess thermal energy could then be thought
of as being transferred down a temperature gradient
primarily by the conduction between colliding molecules
as they vibrate about their equilibrium positions. The
theoretical description for thermal conductivity is then:
k = 2PuNLCy
where P is the probability that energy is transferred on
each collision, u is the vibrational frequency, N the
number of molecules per unit area, L the distance between
molecules, and Cy the heat capacity per molecule.
54
If the quasi-lattice is assumed to be f.c.c., the
above equation is written:
k = /I P Cy/a
where a, the nearest neighbor distance, is related to
3 3
the volume per molecule by a = v2 V or a = /2/p. By
further assuming that both the heat capacity per molecule
Cy, and the probability P are independent of temperature,
Horrocks and McLaughlin differentiated the above equa
tion with respect to temperature, at constant pressure,
and obtained:
1 f 6k 1 6p
1 d In u
6T
v
P
6T
n
3 ( d In V J
where - — — v£— designated a, the coefficient of thermal
p 0 1
1 6k designated A, the temperature
expansion ^ " ' gy 1
dependency of thermal conductivity.
The final term in the right side of the relation
ship describes the change of the vibrational frequency
with respect to volume in the liquid state. This term
is known as Gruneisen’s constant A, and for simple
molecules executing harmonic oscillations adequately
described by the Lennard-Jones 12:6 intermolecular
potential,A can be treated effectively as a constant
(26). With this in mind, the above relationship can
be used as a first order prediction that a linear
relationship exists between —
55
6k
, (X), and the
liquid's coefficient of thermal expansion, a.
Experimental results on nine non-polar liquids
compiled by Horrocks and McLaughlin verified the pre
dicted linearity. This relationship is expressed as
A = - ( - 0 . 0 0 0 2 4 4 + 2 . 2 8 a ) , ° F ' 1
This is the Horrocks-McLaughlin (H-M) relationship and
is independent of temperature and pressure.
When data for the first thirteen non-polar liquids
listed in Table 1-1 were compared with the H-M relation
ship at 77° F, it was found that agreement was generally
quite good as depicted in Figure V-l. Some of the
thermal conductivity versus temperature data of Sakiadis
and Coates were included for the sake of completeness.
Original experimental data were also taken on the last
six hydrocarbon mixtures listed in Table 1-1. Three of
these liquids were well described by the H-M relation
ship and three deviated to varying degrees (refer to
Appendix C for the available properties of these six
mixtures).
B. Correlation for the Deviation of Polar Liquids from
the H-M Relationship
When the temperature dependencies of thermal coidic
tivity (A) and density (a) were plotted at a temperature
56
o
Data of
Sakiadis
& Qoates
13 9
8J»
12 •/
10
+ 55
▲ Gulf Oil # 396
♦ Shell Prem. Dieseline
® Chevron Diesel Fuel
V ZZ -(-0.0002U+ 2.280C)
Horrocks & McLaughlin Relationship
-21
1
4
o
F
x 10
T e m p e r a t u r e D ep e n d e n c y of D en sity
F IG U R E V -l
H O R R O C K S -M c L A U G H L IN R E L A T IO N S H IP a n d N O N -P O L A R L IQ 'S .
of 77° F for the 45 pure liquids listed in Table 1-1, it
was found that the 13 non-polar liquids agreed very well
with the H-M relationship (Figure V-l), while the remain
ing 32 polar liquids generally deviated. The deviations
of the polar liquids are shown in Figure V-2. By in
spection, it can be seen that six of the liquids fall
above the H-M relationship, while most are below the
line. In addition, while most liquids show a negative
coefficient of thermal conductivity, a few show positive
coefficients. Each of these phenomena has been correlated
by examining the magnitude and direction of the deviation
in relation to the polar and associative properties of
each liquid. An additive technique, similar to the
correlation in the previous chapter is to be employed
wherein:
^ ~ ^H-M relationship + ^correction term
The deviations of the polar liquids, AX, have been
correlated by the correlating group 9, where 0 is the
following expression involving the polar and associative
properties of these liquids:
0 ■ v - 0 f^-) * -51 - 4 ]
where:
T em p eratu re Dependency of Therm al Conductivity
58
’ 20
36 •
A -12
• U
•24
021
31 %
17
•13
37 O
• 28
0.0
• 22
• 27
• 29
+12.0
26
+2 3 6 3 5 7 9
T e m p e r a t u r e D ep e n d e n c y of D ensity
F IG U R E V- 2
DEV IA TIO N S of P O L A R LIQUIDS f r o m the H - M R E L A T IO N S H IP
59
As* = Everett's molal entropy of vaporization at
the liquid's normal boiling point (15)
Note: - "i9~ 7 = 1* 000 + 0.035 for 90 non
polar hydrocarbons
M = dipole moment of the molecule
e = dielectric constant of the liquid at 77° F
p/p„ n = density ratio of the liquids at 77° F
2
An explanation of the above properties and their
relation to the deviation of polar liquids is given in
the following chapter.
The correlating group 0 accurately predicts the
deviations of 27 out of the 32 pure polar liquids which
were shown to deviate from the H-M relationship in
Figure V-2. This correlation between AX and 0 is shown
in Figure V-3. The three carboxylic acids (Nos. 43, 44,
45) again could not be correlated. The two other
liquids which could not be correlated are n-Butyraldehyde
(No. 21) and Chloroform (No. 35). In the first case,
only one value exists for the entropy of vaporization and
since its magnitude is not consistent with the lower
aldehydes, its value is suspect (refer to Appendix D-l).
In the second case, precise thermal conductivity versus
temperature data were not available from the literature
(27); nevertheless, Chloroform was included as a repre
sentative of an interesting group of heavy organic liquids.
60
25 •
300
250
22
200
20
150
23 •
• 27
100
•18
H / # 24
15 / • 16
F
J • 20
021
32 •/'
* 7
045
F IG U R E V- 3
C O R R E L A T IO N fo r the D EV IA TIO N of P O L A R LIQUIDS f r o m
the h o r r o c k s - M c L a u g h l i n r e l a t i o n s h i p
61
A least square regression analysis of the solid
data points depicted in Figure V-3 results in a correla
tion of the following form:
AA?7 = (0.598 + 0.046 0) x 10
-4 o c -1
where
0 = 1 AS*
19.7
f • <
p
J
L PHo0 J
1 . 2 ,, x , 1 . 4
(1 + ye)
The above expression is considered to be valid
for all the pure polar and non-polar liquids in Table 1-1
with the exception of the carboxylic acids. It should
be noted that not all the pure liquids listed in
Table 1-1 were included in the correlation depicted in
Figure V-3. This is due only to the fact that not all
the required correlating parameters were available for
all the liquids for which experimental thermal conduc
tivities existed.
When the Horrocks and McLaughlin theoretical
expression for the temperature dependency for non
polar liquids is incorporated into the above correla
tion, a general value for A can be predicted by the
following Equation V:
^pred at 77° F ~ 2.28ot - 0.000244
- (0.598 + 0.046 0 ) x 10”4 Eq. V
62
where A and a are the temperature dependencies of
thermal conductivity and density at 77° F with the units
of reciprocal degrees Fahrenheit.
C. Accuracy of the Predicted Temperature Dependency of
Thermal Conductivity
A complete listing of all the predicted temperature
dependencies of thermal conductivity, as calculated by
Equation V, can be found in Appendix C, column 11. To
find the slope of k vs. t at 77° F, one can either use
the predicted value of thermal conductivity at 77° F
as calculated in Chapter IV, or if reliable experimental
values are available at 77° F, these may be used instead.
The latter approach is recommended if the confidence in
the experimental values at 11° F is high.
1. Experimental Values of Thermal Conductivity
at 17° F as a Reference Point
When the experimental values of thermal
conductivity at 11° F were used in conjunc
tion with the predicted temperature
dependency at 17° F as calculated by Eq. V,
the accuracy of the predicted thermal con
ductivities above 11° F agreed very closely
with experimental results up to 200° F. A
complete listing of the predicted values at
various temperatures is to be found in
Average Absolute P ercent E r r o r , 36 L iquids
63
R E F . P O IN T :
E x p t'l. T h e r m a l
C o n d u c tiv itie s
0 25 50 125 75 100
A T ab o v e R ef. Point; ° F
F IG U R E V -4
P E R C E N T E R R O R in P R E D I C T E D T H E R M A L C O N D U C T IV IT IE S
AS A F U N C T IO N O F T E M P E R A T U R E A B O V E R E F E R E N C E P O IN T
Appendix C, column 5. A summary of the
average per cent error in the predicted
values of thermal conductivity is apparently
a linear function of the temperature span
above the reference point. An extrapolation
of this function suggests that the average
error to be expected in the prediction of
the thermal conductivity of a liquid at
277° F is about 3.5%.
Predicted Values of Thermal Conductivity
at 77° F as a Reference Point
When the predicted values of thermal
conductivity at 77° F as calculated in
Section IV, are used in conjunction with
the predicted temperature dependencies at
77° F, the resulting predictions for the
thermal conductivities at higher temperatures
reflect the uncertainties of the original
prediction of k. For this reason, the same
five liquids which showed unusually high
errors in Section IV will retain the 10 to
34% uncertainties in this section. The
important feature to note is that when the
actual experimental value of k at 77° F was
used in the preceding subsection, the
65
predicted thermal conductivity for all
five of these liquids showed very good
agreement with the experimental results
up to 200° F. This indicates that the
predicted temperature dependency is quite
good, while the predicted thermal conduc
tivities at 77° F may occasionally deviate
to a large degree.
A complete listing of the predicted thermal con
ductivities at various temperatures up to 200° F can be
found in Appendix C, column 6. Only 32 of the 45 liquids
in Table 1-1 have been evaluated. This is due to the
inability to correlate the carboxylic acids and to the
lack of the required physical data for 8 of the liquids.
For water and heavy water, unique values of temperature
dependency at 77° F do not exist since k is not a linear
function of t.
A summary of the average per cent errors can be
found in Figure V-5, as a function of temperature. The
solid line depicts the relationship without the afore
mentioned 5 liquids while the dashed line includes all
32 liquids for which sufficient data were available.
Average Absolute Percent E r r o r
66
A v e ra g e fo r
32 liq u id s
A v e r a g e fo r
28 liq u id s
R E F E R E N C E P O IN T :
C a lc u la te d T h e r m a l
C o n d u c tiv itie s
1 —
--------- 75-------
A T ab o v e Ref. P o in t, °
125 100
F IG U R E V- 5
P E R C E N T E R R O R IN P R E D I C T E D k v s . T AS A
F U N C T IO N O F T E M P E R A T U R E A B O V E R E F E R E N C E P O IN T
CHAPTER VI
DISCUSSION OF THE CORRELATING PARAMETERS
In the two preceding chapters, groups of correlat
ing parameters were presented in order to account for
the deviations of polar liquids from essentially correct
non-polar relationships. The correlating group
2
$ =
AS*
2
P
19.7 J
L ph 9o J
(yi + e)
was presented as a correlation for the deviation of polar
liquids from the modified empirical Weber Equation IV-3
which appeared to be a valid expression for the thermal
conductivity of non-polar liquids at 77° F. The cor
relating group
AS*
G =
19.7
- 1
JH90
1.2 i 4
Cl + Me)
was presented as a description of the deviation of these
same liquids from the theoretical Horrocks and McLaughlin
relationship which rather accurately expressed the
temperature dependency of the thermal conductivity of
non-polar liquids at 77° F.
The four physical properties making up the cor
relating groups are:
67
68
1. AS*, Btu/lb mole ° R--the Everett modifica
tion of the entropy of vaporization at a
liquid’s normal boiling point.
2. e--the dielectric constant of a liquid at
77° F.
3. u e.s.u.--the dipole moment of the individual
molecule; this is a constant for each
molecular species, independent of tempera
ture and state.
4. p, lbm/ft^--the density of a liquid at
77° F.
Each of the physical properties which will be
discussed has a fairly well established relationship
with either or both of the factors which tend to make
polar liquids deviate from non-polar relationships.
These are first of all, the magnitude of the polarity
of the molecules themselves, and secondly, the degree of
intermolecular association between molecules in the
liquid phase through the mechanism of hydrogen bonding.
It is important to note that while all associated liquids
are comprised of polar molecules, not all polar liquids
are associated. It can furthermore be stated, that while
the degree of association and the magnitude of polarity
go hand in hand for many liquids, it is equally true
that some highly associated liquids are comprised of
69
molecules having relatively small dipole moments while
the converse is equally valid. It can thus be seen that
the discussion of the correlating parameters cannot be
undertaken on any simple theoretical basis. From a
semi-empirical approach, however, it will be shown that:
1. The entropy of vaporization tends to
describe the degree of association between
molecules in the liquid phase.
2. The dielectric constant is a function of
many factors, including the degree of
association as well as the magnitude of the
polarity.
3. The dipole moment is a measure of the
magnitude of the polarity of any molecular
species.
4. The density of a liquid tends to reflect
a liquid's degree of association by virtue
of closer molecular packing resulting from
extra hydrogen bonding.
A detailed discussion of each of these physical
properties is given below.
A. Everett's Entropy of Vaporization, AS*
It has been well established that some polar
molecules become associated in the liquid phase through
70
the mechanism of hydrogen bonding (41) . Many decades
before the nature of this mechanism was understood,
scientists had related the degree of association to the
amount of extra energy required to vaporize an associated
liquid relative to an unassociated sample. The earliest
attempt to account for this extra energy was through the
use of Tourton's constant which tended to have the same
value for non-polar liquids, but usually showed higher
values for associated liquids. The standard form of
Trouton's constant is given as the entropy difference be
tween a liquid and its vapor in equilibrium at the normal
boiling point. The principal shortcoming of Tourton's
Rule is that ASy was not truly a constant but tended
to be high for non-polar liquids whose boiling points
were high. Since Trouton first published his observa
tion in 1884 (66), several investigators (3, 15, 21, 23,
47) have made modifications to the basic rule in order
to improve its reliability. A recent modification by
Everett (15) resulted in an entropy of vaporization
which was more nearly constant for most non-polar liquids
no matter what the normal boiling point. Everett pro
posed that instead of considering the process of vaporiza
tion as a liquid evaporating to a saturated vapor, one
should consider a liquid evaporating to a vapor having a
definite molar volume V*. The molar volume in this case
71
does not necessarily have to be in equilibrium with the
remaining liquid. The entropy change for this proposed
process of vaporization is depicted in Figure VI-1 and
is given by the following equation:
AS* = AS.. + Rln ^—
sat
where V is the molar volume of saturated vapor at 1 atm,
5 Be
pressure. With the assumption that the vapor can be
treated as an ideal gas, Everett chose V* to be equal to
22,414 cmVg mole. It then follows thatAS* in English
units is:
40?
AS* = — =z— + Rln — Btu/lb mole ° R
Trouton's Rule Everett's Modif,
V*
sat
AS*
AS
Liquid
Vap. at Sat. Vap. at
P, V ,, T
’ sat *
FIGURE VI-1
Definition and Notation of Entropies of Vaporization
(Vapor assumed to be an ideal gas)
72
Everett verified the constancy of his modified
entropy of vaporization by referring to the latent heats
of vaporization of 90 hydrocarbon liquids listed in the
tables of the American Petroleum Institute Project
No. 44:
AS* = 19.7 + 0.7 Btu/° R lb mole;
ASy = 19.5 + 2.1 Btu/° R lb mole (Trouton's Rule)
Everett's value of 19.7 Btu/lb mole ° R has been
taken in this dissertation as the standard for comparing
the entropies of vaporization for all the liquids in
vestigated. As previously stated, the view has long
been held that if a liquid is associated through the
mechanism of hydrogen bonding, it will require extra
energy in the form of heat to break these bonds and
evaporate a molecule from the liquid state. Before this
extra quantity of heat can be taken as a valid representa
tion of a liquid's degree of association, two important
assumptions must first be investigated. First, the degree
of association in the liquid phase must be independent
of temperature and insensitive to pressure. Second, when
a liquid is evaporated to the vapor state, all inter-
molecular hydrogen bonds are assumed to be broken and the
molecules are unassociated in the vapor phase.
73
The second of the above assumptions can be rather
easily verified by measuring the apparent molecular
weight of the vapor in question. By this technique, and
others, it has long been established that both formic
and acetic acids are associated in the vapor phase (7, 8,
32). It should be recalled from the Introduction to this
dissertation that of all the chemical groups for which
sufficiently accurate data were available, the carboxylic
acids were the only liquids for which adequate correla
tions could not be made. It is here suggested that the
sole reason for this resides in the fact that the
molecules of these liquids are still held together by
hydrogen bonds in their vapor phase. If this statement
is true, it can thus be seen that the value of the
entropy of vaporization of these liquids cannot reflect
the total degree of intermolecular association.
The first assumption regarding the validity of a
liquid's normal boiling point entropy of vaporization
as a measure of the degree of association is more
difficult to verify. This assumption requires that the
degree of association between molecules must be constant
for all temperatures below the normal boiling point.
Many authors of physical chemistry texts have assumed
that the degree of association decreases with rising
temperatures due to increases in the kinetic energy of
74
the molecules. Some investigators (42, 68) have used
this theory to account for the very large viscosity
changes with respect to temperature for some of the
mono-substituted amides. If these, and other authors,
are correct in their contention, then the measure of
a liquid's normal boiling point entropy of vaporization,
relative to the constant value for non-polar liquids,
would not give a valid estimator of the degree of
association at 77° F. This contention, however, is par
tially refuted by Thomas as an outgrowth of his work on
viscosity and molecular association (64, 65).
In 1948 Thomas measured the latent heats of
vaporization versus temperature for the first ten primary,
secondary and tertiary alcohols. The author was able to
isolate the energy requirement for breaking any existing
hydrogen bonds and concluded that for all the alcohols
investigated, the degree of association remained constant
and was not a function of temperature (64). (Refer to
Appendix F for a summary of values.) The author further
stated the belief that for the primary alcohols, the
degree of molecular association in the liquid phase
remains constant nearly to the critical point. In an
extension of this work, Thomas in 1960 investigated the
degree of association of a number of phenols, amides,
their alkyl and halide substitutions, and several other
liquids (65) . (Refer to Appendix F for a summary of
values). In this work the results were not as conclusive.
Thomas reported that for six out of the seventeen liquids
studied, the degree of association remained constant
over the range of vapor pressures from 3 to 760 mm Hg.
For eight other liquids the degree of association
changed by about 10% while for phenol and the cresols,
the change was about 30% over the range of the reported
vapor pressures.
An effort was made to substantiate the work of
Thomas; however, a superficial literature search failed
to reveal any pertinent material. An attempt was next
made to apply the work of Thomas with respect to the
liquids for which he reported changing degrees of
association. Of all the seventeen fluids which Thomas
investigated (see Appendix F), there were sufficiently
accurate literature data available for only m-cresol.
The thermal conductivity of this liquid was reported by
Riedel (52) and this value was compared to the predicted
value at 77° F as calculated by Eq. IV of this disserta
tion using the normal boiling point entropy of vaporiza
tion in the standard manner. The predicted result was
38.6% higher than the experimental thermal conductivity.
By referring to the data of Thomas for this liquid as
listed in Appendix F, it can be assumed that the entropy
76
of vaporization ratio (AS*/19.7) as used in Eq. IV was
311 lower at the normal boiling point than at a vapor
pressure of 3 mm Hg. The lowest vapor pressure reported
by Thomas corresponds to a temperature of 150° F. If the
data of Thomas are extrapolated to 77° F (25° C) (Fig
ure VIII F-l), the molecular association of this liquid
appears to be 50% higher than at the normal boiling point.
When this assumption is incorporated in the required
entropy of vaporization term (AS*/19.7) and Eq. IV is
recalculated, the predicted thermal conductivity of m-
cresol is only 10.7% higher than Riedel's experimental
value at 77° F. While this calculation hardly con
stitutes a proof for either the work of Thomas or the
validity of Eq. IV, it suggests that if more data were
available regarding the degree of liquid association
as a function of temperature, it might be possible to
use the entropy of vaporization ratio with greater con
fidence for a wider range of chemical species. The work
of Thomas to date tends to enhance the concept of using
this term to estimate a liquid's degree of molecular
association, especially insofar as the alcohols are
concerned.
The discussion concerning the entropy of vaporiza
tion as a correlating parameter has been rather involved;
77
fortunately, the argument for the use of the remaining
parameters is considerably more straightforward.
B . The Dielectric Constant, e
The dielectric constant is a macromolecular
physical property of a medium which has a relative effect
upon the electric charge which can be stored on the
plates of a capacitor encompassing that medium. The di
electric constant of a vacuum has been assigned the
value of unity, but for practical purposes, the value
of dry air is essentially equal to the same value. Over
the years many sophisticated devices have been developed
to measure this property in gases and liquids; however,
the one simplest in concept and still widely used is the
parallel plate capacitor.
In this device the capacitance is measured at a
constant potential when the volume between the plates
is first filled with dry air, and then with the medium
to be measured. The dielectric constant is given as:
e = C /C ■
x air
where C and C • refer to the electric capacitance of
x air
the device.
The dielectric constant of a liquid is a function
of many factors such as:
78
1. The number of molecules per unit volume.
2. The temperature.
3. The elastic polarization which results
when the electrons are pulled away from the
nucleus of the molecules due to the induced
electric field between the plates of the
capacitor. This effect has been shown by
Maxwell to be equal to the square of the
refractive index of the medium.
4. The dipole moment of the molecules
comprising the liquid.
5. The interaction of the molecules with
each other.
The first three factors listed above are rather
straightforward. All liquids have a small dielectric
constant due to item (3), the elastic polarization.
Polar liquids have higher dielectric constants due to
item (4) but there is no linear relationship between
these properties since item (5), the interaction of the
molecules, is an independent phenomenon. Until the work
of Kumler (32) in 1934, there was little evidence to
indicate whether the interaction of molecules, which
causes variations in dielectric constants, was a physical
or a chemical phenomenon. Kumler conducted a series of
experiments in which items (1) and (2) above were held
79
constant. By subtracting the square of the refractive
index of each liquid investigated from the measured
dielectric constant, he was able to negate the effect
of elastic polarization. Then by comparing the dielec
tric constants to the dipole moments of a large number of
polar liquids which were known not to be associated,
Kumler concluded from the linear results that the
physical interaction of these molecules were no factor
in the measured dielectric constant. This contention was
reinforced when no linear relationship could be found
for that class of polar liquids which were known to be
associated through the mechanism of intermolecular
hydrogen bonds.
From the work of Kumler, it can be stated that
the dielectric constant is a measure of a particular
liquid’s departure from non-polar behavior by virtue
of both the magnitude of the dipole moment and the
degree of association.
It is suggested that correlations incorporating
the dielectric constant as a parameter might be improved
if the contribution due to elastic polarization were
subtracted. This would render the dielectric constant
a more precise estimator of a liquid's departure from
non-polar behavior. This possible improvement, however,
80
was not investigated for the correlations presented in
this dissertation.
C. The Dipole Moment, p, and Density Ratio p/p^ q
" " ' ■ — '2 ™—
The dipole moment of a molecule is a rather simple
concept, but since it is impossible to measure directly,
its magnitude is often difficult to determine. In con
cept, the dipole moment is a measure of the unequal
electron charge distribution within a particular
molecular species. Symmetrical molecules such as
methane, or linearily symmetrical ones such as decane
have no dipole moment since there is no unequal charge
distribution from one side of the molecule's center to
the other. Polar molecules such as water and the al
cohols, however, are not symmetrical about their centers
and, therefore, have unequal electron distributions,
which can be thought of as a residual electrical charge
at a certain distance from the molecular center. This
charge times the distance comprises the dipole moment of
the molecule, but can only be determined indirectly by
measuring the degree of molecular polarization when an
external electric field is applied across the molecules
in question.
When any molecule is introduced into an external
electric field, the positive nucleus will be attracted
81
to the negative plate while the electrons will be pulled
slightly away from the nucleus in the direction of the
positive plate. Such a distortion of the molecule can
be thought of as polarization into an electric dipole;
the distortion, however, lasts only as long as the
electric field is applied and, therefore, is usually
called elastic polarization.
When polar molecules are introduced into the same
electric field, a further polarization takes place as the
field tends to align the permanent dipoles parallel to
the direction of the external field. The total polariza
tion is thus:
P = P + P
e y
where Pg is the elastic polarization which results from
the electrons being pulled away from the nucleus, and P^
is the orientation polarization resulting from the re
alignment of the permanent dipoles. These two types of
polarization can be differentiated from one another since
the elastic polarization is temperature independent while
the orientation polarization decreases with increasing
temperature.
The total polarization has been theoretically
derived from the dielectric constant of a medium composed
of polar molecules by several authors on the basis of
electromagnetic theory. The simplest relationship was
82
derived by Clausius and Mosotti, and while not rigorously
correct for anisotropic dielectrics has, nevertheless,
been used as a definition of P by many authors of physical
chemistry texts:
total polarization, P, from the measured dielectric
constant, e, is complicated by the fact that many polar
molecules form associated complexes in their liquid state.
For this reason, the molecular weight term, M, is of
unusual importance. The hydrogen bonds between associ
ated polar molecules can often be broken by merely dis
persing the molecules of a liquid phase in a second
carrier fluid. This second liquid is usually dioxane,
benzene or cyclohexane and if the polarization to con
centration ratio is still favorable at the point where
association is no longer discernible, this technique is
often used (37). A more powerful assurance that all the
intermolecular hydrogen bonds are broken is to simply
calculate the total polarization from dielectric data
when the molecules are in the vapor phase. Even
this technique, however, is insufficient to break the
hydrogen bonds between molecules of certain species.
For instance, widely varying degrees of polarization are
Use of the above equation for calculating the
83
reported for the carboxylic acids (37). When measure
ments are conducted in the liquid phase, polarization
values are invariably higher than when the experiments
are conducted by either the dispersed liquid technique
or in the vapor phase. There still i^ little agreement,
however, between the latter techniques and the problem
is usually ascribed to persistent intermolecular
association (7, 32, 33, 37, 41, 45, 47). The exact
molecular geometry into which these carboxylic acids
are associated has, unfortunately, never been determined.
Of these acids, acetic acid appears to have been the
most studied, and as yet there is no conclusive proof
as to how these molecules are associated. There is
considerable proof, however, that these molecules exist
as both cyclic dimers as in Figure VI-2-1 and as open
dimers as in VI-2-2 (7, 33, 47). There is disagreement,
nevertheless, as to which dimer predominates.
0 . . . . H — 0
/ /
R—
w
,C — R
0 — H . . . . 0y
CD
(2)
FIGURE VI-2
Possible Association of Acetic Acid
(Dots indicate hydrogen bonds)
84
It is possible that the correct degree of polariza
tion for acetic acid molecules in an external electric
field has never been reported. There are such conflicting
data as to the relative stability of either dimer that
all polarization data on this and other carboxylic acids
are rather suspect. In fact, the degree of residual
molecular association in dielectric experiments on polar
molecules is perhaps the single greatest source of un
certainty when polarization data are reported. Compila
tions of data such as the one by McClellan (37) abound
in such uncertainties. Fortunately, a great deal of
replication has been done on the highly polar liquids
which comprise the greater portion of this dissertation.
Whenever possible, dipole moment data were taken from
the compilation edited by Weissberger et a^L. (70) When
the required data were not available from this source,
the data values most repeated in the compilation of
McClellan were chosen. In this manner, a certain degree
of assurance can be obtained that the most accurate
polarization data available were employed.
When the total polarization is obtained as
accurately as possible from the Clausius-Mosotti equa
tion, the contribution of the elastic polarization can
be obtained by taking data as a function of temperature
and extrapolating the polarization to zero reciprocal
85
temperature. This extrapolation yields the elastic po
larization which can then be subtracted from the total
polarization at whatever temperature is most convenient,
The dipole moment y can then be evaluated using the
Debye equation for orientation polarization:
2
Pl|= 4/C3W) NU
X VT
3kT
where N is the Avogadro number and k is Boltzman's
constant. The factor 4/(3W) is used to convert molecular
quantities into molar quantities.
The dipole moment is the most conspicuous property
by which polar molecules differ from the non-polar
variety. It has been previously shown, however, that
polar molecules also differ by their ability to form
associated complexes. This phenomenon manifests itself
in both the normal boiling point entropy of vaporization
and the dielectric constant of the liquid phase. A
combination of these three parameters was found to
correlate the deviation of many polar liquids from the
non-polar relationships previously discussed. When the
heavy organic liquids such as carbontetrachloride were
included, however, the correlation based on just the
three parameters appeared to break down. It was then
. . . 86
found to be necessary to incorporate a density ratio term
as well as the existing associative and polar parameters.
The term chosen was the density of the liquid at 77° F
relative to the density of water at the same temperature,
p/pH q * The term has obvious advantages, but perhaps it
would have been better to compare the density of the
polar liquids to an average density of the non-polar
hydrocarbons. This would make sense from the standpoint
that the density of associated polar liquids tends to be
greater by virtue of the closer molecular packing
afforded by intermolecular hydrogen bonding. Such an
arrangement would undoubtedly give the density ratio term
greater weight in the correlation, especially for the
heavy, halogenated hydrocarbons. Whether any discernible
improvement would result in the correlations, however,
remains problematical.
CHAPTER VII
CONCLUSIONS
Most liquid thermal conductivity predictions are
valid only for non-polar liquids in a narrow temperature
range. Some attempts have been made to develop more
general correlations and by far the best of these is the
Robbins and Kingrea estimation published in 1962 (54).
The stated accuracy of this estimation for 70 polar and
non-polar liquids is about 41 for a temperature range
extending from 68 to over 200° F. When later and more
reliable thermal conductivity data are used for com
parisons, the average accuracy drops to about 6%. While
this accuracy is acceptable by engineering standards,
there are several limitations and drawbacks to its wide
spread use.
Two correlations have been developed in this
dissertation for the general prediction of liquid thermal
conductivities as a function of temperature. These are
based upon earlier relationships valid only for non
polar liquids under certain restricted conditions. In
87
88
each case, these older predictions have been modified
to apply to polar as well as non-polar liquids by in
corporating suitable terms comprised of polar, associative
and dielectric properties of these liquids.
The first relationship predicts the thermal con
ductivity of liquids at 77° F and is based upon the
Weber Equation published in 1880. The second relation
ship predicts the linear temperature dependency of
dk/dT at 77° F and is based upon the theoretical work
of Horrocks and McLaughlin published in 1960 (24, 25, 26).
These correlations were developed with the aid of
reliable thermal conductivity data obtained from a new
transient hot-wire apparatus patterned after the compara
tive device developed by Grassmann in 1960 (18).
The thermal conductivity temperature dependency
relationship developed in Chapter V predicts coefficients
with an accuracy of about 7%, These coefficients have
been checked against all 39 polar and non-polar liquids
listed in Table 1-1 for which the required correlating
physical properties are available. With experimental
thermal conductivity values at 77° F serving as the
reference point, values at 277° F have been predicted for
36 out of the 39 liquids with an average accuracy of
3.5%. The three liquids which were excluded are
carboxylic acids and these are believed to lie outside
the correlation due to molecular association which per
sists into the vapor phase.
A second correlation has been developed for use
in conjunction with the temperature dependency relation
ship if reliable k data at 77° F are not available.
This correlation, based upon the Weber Equation, has
been tested for all 38 liquids listed in Table 1-1 for
which the required correlating properties are available
The predictive accuracy for thermal conductivities at
77° F for 31 out of the 38 liquids is 3.3%. The remain
ing seven liquids are primarily dense, halogenated
hydrocarbons which show large deviations ranging from
11 to 36%.
These two correlations, taken together, are some
what easier to use than the Robbins and Kingrea estima
tion and are of equal or greater accuracy and, further
more, extended over a greater range in temperature.
APPENDICES
A. DESCRIPTION OF THE TRANSIENT HOT-WIRE
THERMAL CONDUCTIVITY APPARATUS
B. EXPERIMENTAL RESULTS
C. TABLES OF EXPERIMENTAL AND CALCULATED
DATA
D. COLLECTED PHYSICAL PROPERTIES OF LIQUIDS
E. OBTAINMENT OF THERMAL CONDUCTIVITY
CORRELATIONS
F. DEGREE OF MOLECULAR ASSOCIATION OF SOME
LIQUIDS AS A FUNCTION OF TEMPERATURE
90
91
APPENDIX A
DESCRIPTION OF THE TRANSIENT HOT-WIRE THERMAL
CONDUCTIVITY APPARATUS
The transient hot-wire thermal conductivity
apparatus used for the collection of experimental data
was a relative type of device patterned after the work of
Grassmann done in 1960 (18). The transient temperature
response of a hot-wire element was calibrated using the
thermal conductivity data of toluene as reported by
Ziebland in 1961 (71) . Since the temperature response
of a hot-wire element is a well defined logarithmic
function of time, Grassmann was able to linearize this
function by plotting it against a similar log function
from a second hot-wire system. The thermal conductivity
apparatus thus consists of two parallel hot-wire systems.
The theoretical and operating principles of this device
were previously presented in Chapter III; a detailed
physical description is given below.
1. Description of the Hot-Wire Cell
The design of the hot-wire thermal conductivity
cell is such that a thin wire element can be vertically
suspended under tension along the center line of an
92
inclosed steel cylinder. Such a cell was designed, built
and implemented at the University of Southern California
and is depicted in Figure A-l. Incorporated with the
cell is a pressurization system which allows nitrogen to
be indirectly applied to the test liquid through an inter
vening volume of mercury. The entire system shown in
Figure A-l is submerged in a controlled temperature oil
bath. As the oil bath is heated to a new equilibrium
temperature level, the test liquid expands and forces
the mercury into its expansion vessel. Each vessel has
1/4 the capacity of the hot-wire cell and is sufficient
to contain the expansion of most fluids from ambient
temperature to 450° F.
The cell is fabricated from type 316 stainless
steel Shelby tubing and can withstand 500 psig at 500° F.
The mercury vessels and connecting tubes are made from
316 SS AN tubing and fittings.
The apparatus consists of four cells and mercury
systems with a common nitrogen pressure manifold. The
hot-wire elements are silver-soldered to 14 gauge copper
leads and are held in tension by the lead weights shown
in Figure A-l. A pressure seal is maintained around
these copper leads by means of Conax fittings which are
welded to the top flange of the cell. The flange and hot
wire assembly can be removed from the cell for loading
93
100 to 500 p sig
N itro g e n
E l e c t r i c a l
L e a d s \ V
14 ga. C u ^
E x p a n sio n
V e s s e l
Vent
C ell
1 m il Ir
H ot- W ire
E l e m e n t
W eight,
7 g r a m s
M e r c u r y
F IG U R E A - l
T H E R M A L C O N D U C T IV IT Y C E L L an d P R E S S U R E S Y S T E M
94
purposes and suspended in an ultrasonic solvent tank
for cleaning between experimental runs.
When these cells were equipped with high-strength
Iridium elements, 1 mil in diameter, no element was
broken during nine months of continuous use and fifteen
months of intermittent operation. The only problem
associated with these cells occurs when the Teflon
gasket, used to seal the top flange of the cell, becomes
distorted due to its cold-flow characteristics and
causes leakage of the test liquid. A few experimental
runs had to be terminated due to this problem and a more
applicable gasketing material or system should be
provided. Aside from this problem, the reliability of
the hot-wire cell system was more than adequate over the
9-month experimental period.
2. Apparatus Circuitry and Operating Procedure
The circuitry of the transient hot-wire thermal
conductivity apparatus consists essentially of two
Wheatstone bridges, two DC power supplies and a X-Y
recorder for measuring the voltage changes produced
by the bridge circuits. These voltage changes are
generated by resistance heating of the thin hot-wire
elements which comprise one arm of each bridge and which
are immersed in fluids initially in thermal equilibrium
with their surroundings. Under these conditions, the
95
voltage output from each bridge is inversely proportional
to the thermal conductivity of the liquid surrounding
each hot wire. A theoretical justification of this
statement was previously given in Chapter III. A more
detailed discussion as to the practical limitations,
however, will be given after the circuitry itself is
described.
A schematic circuit diagram of the transient
thermal conductivity apparatus is shown in Figure A-2;
a list of its components is given in Table A-l.
In the operation of the apparatus depicted in
Figure A-2, the two Wheatstone bridges are first balanced
by passing a feeble DC current from the power supplies,
through the shunt resistors R5 and into the bridge
circuits. In these circuits, resistors R2 and R3 form
a high impedance barrier which channels 99% of the current
through resistors R1 and R4. The resistors R1 are com
posed of the thin Iridium elements, 1 mil in diameter,
while resistors R4 are parallel arrangements of high
impedance variable resistors R4b and low impedance con-
stantan resistors R4a for providing a constant resistance
path into each Iridium element. When the two bridges
are balanced by using the variable resistors so that no
voltage output is indicated on the microvoltmeter, the
apparatus is ready for operation.
96
X -Y
R e c o r d e r
/ 1 /1
R 4a R 4a
R 4b
R3 R3
R2
C E L L C E L L
R5 R5 S2j
S4 S3
R6
F IG U R E A - 2
T R A N S IE N T H O T -W IR E A P P A R A T U S fo r the M E A S U R E M E N T of
LIQ U ID T H E R M A L C O N D U C T IV IT IE S
TABLE A- 1
C o m p o n e n ts in C i r c u i t D i a g r a m
R1 - M e a s u r in g h o t - w i r e e l e m e n t s ; 1 m il d i a m e t e r
I r id i u m w ir e 6 in. lo n g . A p p r o x . 28 o h m s
R2 - 2000 o h m s , m e ta l f ilm r e s i s t o r s
R3 - 3000 o h m s , m e ta l f il m r e s i s t o r s
R x4a - C o n s ta n ta n w ir e in c o n s t a n t te m p , bath,
(2 6. 5) o h m s .
R x4b - V a r ia b l e H elip o t, 0 -5 0 0 ohm s
R y 4 a - C o n s ta n ta n w ir e in c o n s ta n t t e m p , bath w ith
14 c e n t e r ta p s (24-34) o hm s
R y4b - V a r ia b l e H elip o t, 0 -1 0 0 0 o h m s
R5 - 1200 o h m s , c a r b o n r e s i s t o r s
R6 - 900 o h m s , c a rb o n r e s i s t o r
51 - M a in c i r c u i t sw itc h
52 - Shunt s w itc h for p a s s i n g feeb le c u r r e n t to
b r id g e c i r c u i t s
53 - B a la n c e p o w e r s w itc h
54 - Shunt s w itc h for b a la n c in g p o w e r su p p lie s
55 - Tw o s w itc h e s for b a la n c in g x a n d y W h e a t
stone b rid g e c i r c u i t s
56 - R e c o r d sw itc h
P x , P y - R e g u la te d DC p o w e r su p p lie s, 0 - 3 6 v olts,
0-1 1/2 a m p s , (o p e r a te d at 2. 8 v o lts)
X -Y R e c o r d e r - M o s e le y M od, 7000A ( o p e ra te d a t
a s e n s itiv ity of 0. 2 m v p e r inch)
M i c r o - v o l t m e t e r - H e w l e t t - P a c k a r d M od. 425A (used
fo r b a la n c in g the b r id g e c i r c u its )
(o p e ra te d a t a s e n s iti v ity of 0. 1
m illiv o lts )
98
In the operation of this thermal conductivity
apparatus, the Y cell is first filled with the calibra
tion liquid toluene and the X cell with any liquid of
high viscosity. This latter property is necessary in
order to insure that the X cell will not become limiting
with respect to the onset of natural convection. The
liquid chosen for this work was Chevron Alta Vis 530 with
a viscosity of 11,000 cps at 77° F. The thermal con
ductivity of this liquid as a function of temperature
is given in Appendix B-3 and other properties are listed
at the end of Appendix D-l. The X cell was maintained
at a constant temperature of 107° F while the Y cell
was varied from 60° F to 250° F. The transient voltage
response of this toluene (Y cell)-Alta Vis (X cell)
system were recorded at many equilibrated temperature
levels of the Y cell as a series of straight lines on
the X-Y recorder. An example of this type of raw data
is given in Figure A-3. The slopes of these lines,
multiplied by the thermal conductivity of toluene
(shown in Figure A-4), constitute the calibration con
stants for each particular temperature. The calibration
points as a function of temperature are dependent upon
the resistance changes of the hot-wire elements.
While the calibration curves for Invar, Platinum, and
Platinum-Iridium elements were linear functions of
f
F IG U R E A - 3
S E R IE S O F A C T U A L X -Y D A T A R E C O R D IN G S F O R T O L U E N E a t 95 ° F
to
to
THERMAL CONDUCTIVITY O F T O L U E N E
THERM AL CONDUCTIVITY, B T U /h r ft ° F
0
cl
jo
W
>
1
001
$
ft
101
temperature, the calibration curve for pure Iridium was
slightly curved as shown in Figure A-5.
Once the calibration curve has been obtained for
the Y cell, the thermal conductivity of any new liquid
inthis cell is obtained by merely recording the transient
voltage responses for the new liquid, in conjunction with
the constant X cell, and dividing the slopes of the
linear portion obtained into the previously determined
cell constant.
, _ cell constant _ (^toluene)(si°?e °f toluene)
un nown slope of unknown slope of unknown
The thermal conductivity of any liquid can be
obtained within the limitations outlined on page 31 of
Chapter III.
CELL CO NSTA N T, K S
! i lt: r
050
046
140 160 180
T E M P E R A T U R E ° F
F IG U R E A - 5
C A L IB R A T IO N O F C E L L # 1 , IRIDIUM S E T # 3
102
103
3. Accuracy of Experimental Results
Because of the paucity of reliable existing
thermal conductivity data, a quantitative measure of the
accuracy of experimental results is difficult to obtain.
There are, however, two qualitative areas which can be
examined which pertain indirectly to the accuracy of
any experimental data.
Examination of the experimental thermal conduc
tivity data, as presented in Appendix B, shows that in
no case does the experimental scatter exceed + 2% for any
liquid incorporated into the correlations of this dis
sertation. For the most part, the experimental scatter
is on the order of + 1% with each data point represent
ing the arithmetic average of 7 to 10 experimental deter
minations. The 95% confidence limit on each of these
data points usually fell below +0.3% with a point rarely
exceeding the +1% value. Only in the case of 2-Nitro-
propane (Liq. No. 30) was a significant amount of data
rejected. In this case, the first two experiments com
prising nine data points were discarded. The weight of
evidence compiled from four later experiments encompass
ing seventeen data points was the reason this action was
taken. One further note on this liquid is in order;
2-Nitropropane was the only liquid that was not of
reagent grade and that did not come from a sealed bottle
104
obtained from the U.S.C. chemical stockroom (see Appendix
B-2) .
When the experimental data are examined in conjunc
tion with the literature data reported by other in
vestigators, two facts become apparent. A great deal of
uncertainty exists in the field of liquid thermal con
ductivity, but generally speaking, the data of Riedel
(52, 53), Jobst (28), and Grassmann (19) nearly always
coincide to within 2% of the experimental data reported
in Appendix B. This fact, coupled with the excellent
reproducibility of the experimental results, indicates
that the experimental data are qf a relatively high order
of precision. It should be noted, further, that a sig
nificant amount of literature data exists for both n-
Hexane and ethanol and that these liquids were used as
a check on the accuracy of the experimental apparatus.
Data on n-Hexane are especially interesting in that
results were accumulated over a one-year span using three
different types of measuring elements (see Appendix B-l).
The total scatter on 18 data points collected over a
temperature span of 70 to 200° F was +1.37% and -1.66%.
It should also be noted that n-Hexane is a rather dif
ficult liquid to measure since the onset of natural con
vection occurs rather rapidly due to its low viscosity
and its relatively high coefficient of expansion.
105
In summary, the claimed overall precision is
+_2% with an overall accuracy of +4% based upon the works
of a few respected experimentalists. While this claim
is based solely upon the experimental results, a further
insight into the reliability of a hot-wire apparatus such
as employed herein can be obtained by referring to the
analytical and empirical investigations which Horrocks
and McLaughlin (26) conducted in conjunction with their
work.
4. Reliability of Results Based on Analytical Consider
ations
Horrocks and McLaughlin (26) obtained experimental
thermal conductivities on a number of liquids by record
ing the transient temperature changes of a hot-wire
apparatus rather similar to the device employed herein.
The primary difference in the apparatus of these authors
compared to that of Grassmann was that they employed
only a single 6 inch long, 0.001 inch diameter platinum
wire as an arm of a single Wheatstone bridge circuit.
Furthermore, they determined the thermal conductivity of
a liquid on an absolute basis by measuring not only the
temperature changes of the measuring element, but the
heat input to the wire itself. The authors used the
same equation which was developed in Chapter III, namely
Eq. 111-2:
and investigated many possible perturbations to its
accurate employment. In summary, the perturbations
analytically investigated by these authors were:
1. Effect of radiation from the wire.
(Shown to be negligible.)
2. Effect of the thermal capacity of the
heater in relation to thermal capacity of
the liquid. (Maximum possible error = 0.3%)
Note: This source of error is somewhat
canceled by use of a calibration
fluid of similar heat capacity to
the majority of unknown liquids.
3. Effect of finite wire diameter. (No effect
for experimental periods greater than 0.1
second.)
4. Effect of a bounded liquid sample. (Maximum
possible error is 0.4%; however, for the
usual time periods employed the average
error is 0.01%.)
5. Effect of finite wire length. (For a 6"
wire, effect is negligible, 0.0005%.)
6. Effect of heat conduction through the
soldered leads holding the thin wire element.
107
(Maximum error encountered in authors' work
was for 2° C temperature rise in 30 seconds
of heat input; this results in a 0.01% error.
This can be compared to a 4° C temperature
rise in the present Iridium element, but in
a time period of less than 10 seconds.)
The total possible error envisioned by Horrocks
and McLaughlin in employing Eq. 111-2 for the experi
mental determination of liquid thermal conductivities
was on the order of +_ 0.25% (26).
108
APPENDIX B
GRAPHICAL PRESENTATION OF EXPERIMENTAL RESULTS
FOR THE THERMAL CONDUCTIVITY OF LIQUIDS
B-l) Experimental Results on Non-Polar Liquids
B-2) Experimental Results on Polar Liquids
B-3) Experimental Results on Liquids Which
Could Not Be Incorporated into the
Correlations for Various Stated Reasons
Notes concerning the presented results:
1) Experimental numbers refer to measurements
on a single liquid sample.
2) Experiments consist of data taken from at
least two or more heating and cooling
cycles with about 10 to 12 data points per
experiment.
3) Data points are an average of ten repetitious
measurements. The 95% confidence limit on
each data point range from less than 1/4%
to about 1%, depending upon the liquid's
viscosity and coefficient of expansion.
4) Whenever possible, literature data are also
depicted.
109
B-l) Experimental Results
No. Liquid
3 n-hexane
5 methyl-
cyclohexane
9 n-heptane
12 n-decane
on Non-Polar Liquids
n * n *
D D
Exp. Lit.
1.3766 1.3754
1.4229 1.4235
1.3876
1.4109 1.4120
Reference liquid: toluene 1.4964 1.4969
* Refractive index at 20° C
Exp. values were obtained from a Baush 8
Lomb Abbe Refractometer, Model #56.
Lit. values were obtained from Handbook
of Chemistry and Physics, 40th ed., Chemical
Rubber Publishing Co., Cleveland, Ohio, 1959.
THERMAL CONDUCTIVITY, BTU /hr ft ° F
H
a
is
S
>
r
o
o
a
O
cj
o
H
kJ
O
G
a
w
x
>
a
w
{
ugguiHI i
'JL
Oil
THERMAL CONDUCTIVITY O F METHYLCYCLOHEXANE
T H E R M A L C O N D U C T IV IT Y , B T U / h r ft ° F
O O © O O O
ITT
THERMAL CONDUC TIVITY, BTU /hr ft ° F
■ . p . - J v r :
Sit t t h
St
EpjxR
tarns
t t t !
r 'H'H
V »-rr
rS£ Hi?
“ SHHSi
ill ii52^£E±S
069
160 180 200
TEMPERATURE ° F
THERMAL CONDUCTIVITY OF n-HEPTANE
112
THERMAL C O N D U C TIV ITY , BTU /hr ft °
. 078i
I I
=W4fi?
ua
i - X mT
. 070
x r - m n t :
i...
islgg
•ass
i
140 166“ 180 200
T E M P E R A T U R E ° F
220
THERMAL CONDUCTIVITY OF n-DECANE
113
2)
Experimental Results on Polar Liquids
nn* nn*
No. Liquid
Exp*
Li?.
15 ethanol 1.3624 (18°
18 cyclohexanol 1.4656 (23°
21 n-butraldehyde 1.3850 1.3843
28 1,2-propanediol 1.4323
30 2-nitropropane 1.3997** 1.3941
31 nitrobenzene 1.5522 1.5529
32 m-nitrotoluene 1.5468 1.5475
33 benzonitrile 1.5286 1.5289
34 carbontetra-
chloride
42 tetrachloro-
ethylene
1.4630 (15'
1.5053
* Refractive index at 20° C
Refer to page 109 for notes concerning
Exp. and Lit. values.
** Technical Grade
THERMAL C O N D U C T IV IT Y , B T U /hr ft
mm
■ H U T t o !
H H t S l i
D&bTJ
i r t i - r U
t j*}±3
£553
160 180 200
T E M P E R A T U R E ° F
THERMAL CONDUCTIVITY OF ETHANOL
115
THERMAL CO N D U C TIV ITY , BTU /hr ft
iH
h. 079
rWsi
W a r «ii
140 160“ 180 200
T E M P E R A T U R E ° F
THERMAL CONDUCTIVITY OF CYCLOHEXANOL
116
T H E R M A L C O N D U C T IV IT Y , B T U ? H R F T
o o o o o o
0s - O ' - J -0 00 oo
4k 0 0 N o o
(is r < :::si:
lii , r ' i* i i
L II
THERMAL CONDUCTIVITY, BTU/hr ft
“ H i - H r i
m
TEMPERATURE ° F
THERMAL CONDUCTIVITY OF 1, 2-PROPANEDIOL (PROPYLENE GLYCOL)
118
THERMAL C O N D U CTIV ITY , B TU /ft h r
f > 4
O
. 078
. 074
070
066
062
058
J l T t ' t * n =
— bn
"!' r. i :
160 180 200
T E M P E R A T U R E ° F
THERMAL CONDUCTIVITY OF 2-NIT RO PRO PANE
119
THERMAL CONDUCTIVITY, BTU/hr ft
• H i
m
w . n i T u
X T L h ' X - I ' p
i i r
r * - + - f
’ JW55
imTEH
jj F i f L I F i F j
146 160 180 200
TEMPERATURE ° F
THERMAL CONDUCTIVITY OF NITROBENZENE
120
THERMAL C O N D U C T IV IT Y , B T U /hr ft ° F
IS
31
n £ H -;rr
m m
ud I t t R
f' 4 -r-
tm. -flH
rrf -H
rvf y
nmn
P S
$
m m m m
i iitl xrn'
5 i t r
SifilS
-rrt-rn
100 120 140 160 180 200
T E M P E R A T U R E ° F
220 240
THERMAL CONDUCTIVITY OF m-NITROTOLUENE
121
THERMAL C O N D U C T IV IT Y , B T U / h r f t ° F
084
082
080
078
076
074
-T4 i i i n - m :
1 1 1
mjttS
ih t i:)^4
H - 4 + H -T
1
rmitn
- p - U
I
r o ± m i
160 180
T E M P E R A T U R E
THERMAL CONDUCTIVITY OF BENZONITRILE
122
THERMAL C O N D U C T IV IT Y , . B T U / h r . f t
0
070
066 f
062
058
054'
.050
I
i 120 140
T E M P E R A T U R E ° F
THERMAL CONDUCTIVITY OF CARBON TETRACHLORIDE
TEMPERATURE ° F
THERMAL CONDUCTIVITY OF TETRACHLOROETHYLENE
124
125
B-3) Experimental Results on Other Liquids
n
No.
46
47
48
49
50
Liquid
D
Exp,
n
D
Lit.
1,3-butanediol 1.4391
1,4-butanediol
N,N-dimethyl-
formamide
N,N-dimethyl-
acetamide
N-methyl-
acetamide
1.4298
1.4379
Reasons for Exclud
ing Results from the
Correlations
Data on dipole moment
not available
Data on entropy of
vaporization not
available
Expt'l. k data very
poor
Data on entropy of
vaporization not
available
Liquid has consider
able electrical con
ductivity. This is
believed to result
in spurious experi
mental data
51 DuPont oil
52 Gulf Harmony
#204
53 Chevron Alta
Vis #530
54 Gulf Oil #896
Hydrocarbon mixture,
critical tempera
ture not known
Hydrocarbon mixture,
critical tempera
ture not known
Hydrocarbon mixture,
critical temperature
and mol. wt. not
known
Hydrocarbon mixture,
critical temperature
not known
*Refractive index at 20° C
Refer to p. 109 for notes on Exp. and Lit. values.
126
B-3)
No.
55
56
Experimental Results on Other Liquids (cont.)
Reasons for Excluding
Results from the
Correlations_____
Hydrocarbon mixture,
critical temperature
not known
Chevron Diesel Fuel Hydrocarbon mixture,
critical temperature
not known
Liquid
Shell Prem. Grade
Dieseline
TEMPERATURE ° F
THERMAL CONDUCTIVITY OF 1, 3 - BUTANEDIOL
THERMAL CONDUCTIVITY BTU/hr ft
.128
o
I r . Iu.7*
■■ ■■■*■ »np«
■* intimniiiiiinu
■it ..n:i ^.'.iiiurii
i:
.116 i
.112
.108
140 160 180 200
TEMPERATURE ° F
THERMAL CONDUCTIVITY OF 1, 4-BUTANEDIOL
128
80 100 120 140 - 160 180 200 220
TEMPERATURE ° F
THERMAL CONDUCTIVITY OF N, N- DIME THY LFORM AMIDE
240
THERMAL CONDUCTIVITY BTU/hr ft
100
I
I * 5 5 f c # S S S S S ' -
65 80 jjO O 120 1$5“ 160 180 200
TEMPERATURE °F
THERMAL CONDUCTIVITY OF N, N-DIMETHYLACETAMIDE
130
THERMAL CONDUCTIVITY B T U / h r f t ° F
1
TEM PERATURE
THERMAL CONDUCTIVITY OF N-METHYLACETAMIDE
131
THERMAL CONDUCTIVITY BTU/hr ft ° F
» * • • •
unr.u:
---lit** i
T - r r t f c i T
L d r i i i T f -
-i-* i
ESSSSr mtmr
SE ESSES
iiiiiii H i
180 200
TEM PERATURE ° ’
THERMAL CONDUCTIVITY OF DuPONT OIL
132
THERMAL CONDUCTIVITY BTU/hr ft
k .094
. 092
. 090
088
086
084
£3
I
m l | m n u < n i i i i i j M
iniiiiiiiiiuiiuiiiiHt
160 180 200
TEMPERATURE ° F
THERMAL CONDUCTIVITY OF GULF HARMONY #204
133
THERMAL CONDUCTIVITY BTU/hr ft
o • 072
: : : t nrt
8 0
i i i z i i i i i i i
100 140 160 180 200
TEMPERATURE of
220 240
THERMAL CONDUCTIVITY OF CHEVRON ALTA VIS 530
134
THERMAL CONDUCTIVITY B T U / h r f t ° F
m
:tSS85«;^:8S33^
■SfrI*S5erh''1tf *55fc
z xr\. n::
TEMPERATURE °F
THERMAL CONDUCTIVITY OF GULF OIL # 896
135
THERMAL CONDUCTIVITY B TU /hr ft
i
T E M P E R A T U R E ° F
T H E R M A L CO N D U C TIV ITY O F S H E L L P R E M IU M D IE S E L IN E
136
THERMAL CONDUCTIVITY B T U / h r f t
E n. 072
T E M P E R A T U R E
THERMAL CONDUCTIVITY OF CHEVRON DIESEL FUEL
137
138
APPENDIX C
IDENTIFICATION OF COLUMNS IN THE FOLLOWING TABLES OF
EXPERIMENTAL AND CALCULATED DATA
Col. No.
1 Number refers to the liquid's number as listed
in Table #1; temperature in 0 F at which
data are recorded.
2 Experimental values of thermal conductivity
in Btu/hr ft ° F.
3 Name of reference for thermal conductivity
data, numbers refer to the Bibliography.
4 Predicted value of thermal conductivity at
77° F as calculated in Section IV by Eq. IV-4
ky? = 0.00433TcpCp (p/M)1/3 - 0.00088$
4a Per cent diff. between col. 2 and col. 4
[(calc. - exp.)/exp.] x 100.
5 Predicted values of thermal conductivity at
various temperatures as calculated in Section v
by using the experimental k data at 77° F
as a reference point:
^calc 0
5a
6
6a
7
8
9
10
139
2 = kexp 0 77 + kexp 0 77 (Xcalc 0 77)
17= - [-0.000244 + 2.88a - (0.598 + 0.0460) x 10~4]
Per cent diff. between col. 2 and col. 5.
Predicted values of thermal conductivity at
various temperatures as calculated in Sec
tion V by using the predicted values of
k 0 77° F as a reference point.
k2 = kpred. @ 77 (1 + Xcalc 0 77^
Per cent diff. between col. 2 and col. 6.
Temperature dependency of density at 77° F:
a ?7 = 1 /p (dp / d t ) , ° F ' 1
Theoretical temperature dependency of thermal
conductivity at 77° F as calculated by the
Horrocks and McLaughlin Relationship:
Xtheo 6 77 - -lACdk/dt), “ F'1
= - (-0.000244 + 2.28a)
Experimental values of the temperature
dependency of thermal conductivity (refer
to references in col. 3)
Correlation parameter for the temperature
dependency of thermal conductivity at 77° F:
0 77 = (AS*/19.7 - 1) Cp/pH20)1'2 Cl + ye)
140
1.4
11 Calculated values of the temperature dependency
of thermal conductivity at 77° F as cal
culated in Section V:
X , nn = - [-0.000244 + 2.28a - (0.598 + 0 . 0 4 6 q ) x 10" 4 ]
calc @77
12 Correlation parameter for the prediction of
the thermal conductivity at 77° F as cal
culated in Section IV:
477 = (AS*/19.7)2(p/PH^0)^(y + e)
T A B L E C - l
T A B L E O F E X P E R IM E N T A L AND C A L C U L A T E D DATA
I 2 3 4 4a 5 5a 6 6a 7 8
9 10 11 12
No.
&
°F
Kexp
Btu
Ref.
&
K 1
calc
a t 77°F
%
E r r . ^halc
%
E r r . ^halc
%
E r r .
“ 77
V I
K 104
A theo
V 1
x 104
A exp
v i
x 10*
9
77
A calc
V 1 4
X 10*
$
77
hr. ftT^F
No.
#1 R ied el
77
100
120
150
200
.0 6 5 8 3
53
.0 6 4 6 8 - 1 .7 .06583
.0 6 3 2 6
.0 6 1 0 2
.05766
.05207
0. 0 .0 6 4 6 8
.0 6 2 1 8
.0 6 0 0 0
.05673
.0 5 1 2 9
- 1 .7 8. 72 - 1 7 .4 4 - . 001 - 1 6 .8 4 0. 72
#2
77
100
120
150
200
.07531
.07283
.0 6 7 3 8
.0 6 1 9 7
S ak iad is
56
.0 6 8 6 9 - 8 .8 .07531
.0 7 2 9 0
.0 7 0 8 0
.06766
.0 6 2 4 2
0. 0
+ 0. 1
+ 0 .4
+ 0 .7
.0 6 8 6 9
.0 6 6 5 2
.0 6 4 6 2
.0 6 1 7 9
.0 5 7 0 6
- 8 .8
- 8 .7
- 8 .3
- 7 .9
7 .3 7 - 1 4 .3 6
-1 4 .4 9 . 006 - 1 3 .7 6 1. 10
#3
77
100
120
150
200
.0 6 8 2 3
.0 6 5 9 3
.0 6 3 8 8
.0 6 0 8 3
.0 5 5 7 7
M alian
.0 6 7 5 2 - 1 .0 .06823
.0 6 5 9 2
.0 6 3 9 2
.0 6 0 9 0
.0 5 8 8 8
0 .0
- 0 . 0
+ 0. 1
+ 0. 1
+ 0 .2
.0 6 7 5 2
.0 6 5 2 6
.0 6 3 2 9
.0 6 0 3 4
.0 5 5 4 3
- 1 .0
- 1 .0
- 0 .9
- 0 .8
- 0 .6
7. 72 - 1 5 .1 6 - 1 5 .1 4
.......
. 000 - 1 4 .5 6 0. 82
1 2 3 4 4a 5 5a 6 6a 7 8
9
10 11 12
H H o r r o c k s
77 .0 6 8 9 0 26 .06962 1. 0 .0 6 8 9 0 0. 0 .06962 1 .0 6. 54 -1 2 .4 7 -11. 51 . 004 -11. 87 1.12
100 .0 6 7 1 0 .0 6 7 0 0 -0. 2 .06772 0. 9
120 .06552 .0 6 5 3 4 -0. 3 .06607 0. 8
150 .0 6 3 1 0 .0 6 2 8 6 -0. 4 .0 6 3 5 9 0. 8
200 .0 5 9 1 5 .05872 -0. 7 .0 5 9 4 5 0. 5
#5 S akiadis
77 .06450 56 .0 6 4 7 3 0. 4 .06450 0. 0 .0 6 4 7 3 0 .4 7. 93 - 1 5 .0 4 -15. 47 -. 006 -15. 64 0. 82
100 .0 6 1 6 0 .06225 1. 1 .0 6 2 4 9 1 .4
120 .0 6 0 2 9 .0 6 0 5 4
150 .0 5 6 6 0 .05735 1. 3 . 05.762 1 .8
200
.0 5 1 1 9 .0 5 2 4 5 2. 5 .05275 3. 0
#6 S ak iad is
77 .06023 56 .0 6 4 3 4 6. 8 .0 6 0 2 3 0. 0 .0 6 4 3 4 6. 8 6. 46 -12. 29 -15. 46 - .0 1 2 - 1 1 .6 9 0. 83
100 .0 5 9 3 0
.0 5 8 5 9
- 1 .2 .06261 5. 6
120 .0 5 7 1 6 .06111 4. 6
150 .0 5 5 3 0 .05503 -0. 5 ' .05785 1. 5
200 .0 5 1 9 6 .0 5 1 6 0 -0. 4 .05275
#7 S ak ia d is
77 .0 6 8 8 8 56 .07030 2 . 0 .06888 0. 0 .0 7 0 3 0 2. 0 7. 02 -13. 57 -14. 49 -. 004 -1 2 .9 7 1. 09
100 .06650 .06680 0. 4 .06820 2. 6
120
.0 6 4 9 9 .06638
1
I —1
- p >
fO
TABLE C-l (Cont.d.)
1 2 3 4 4a 5 5a 6 6a
150 .0 6 1 5 0 .06228 1. 3 .06335 4. 7
200 .05645 .0 5 7 7 6 2. 3
.0 5 9 0 9
#8 M alian
77 .06421 .07235 13. .06421 0. 0 .07235 13.
100 .0 6 2 4 3 .06252 0. 1 .07047 13.
120 .0 6 0 9 0 .06105 0. 2 .0 6 8 8 4 13.
150 .0 5 8 6 0 .0 5 8 8 5 0. 4 .0 6 6 3 9 13.
200 .0 5 4 7 6 .0 5 5 1 8 0. 8 .06231 14.
#9 M alian
77 .0 7 1 1 6 .07052 -0. 9 .0 7 1 1 6 0. 0 .07052 -0. 9
100 .06922 .0 6 9 0 7 -0. 2 .0 6 8 4 7 -1. 1
120 .0 6 7 5 3 .0 6 7 2 5 -0. 4 .0 6 6 6 9 - 1 . 2
150 .06501 .06452 -0. 8 .06402 - 1 . 5
200 .06081 .0 5 9 9 8 -1. 4 .05957 -2. 0
#10 Sakiadis
77 .0 7 3 5 2 5 6 .0 7 2 8 0 - 1 . 0 .07352 0. 0 .0 7 2 8 0 - 1 . 0
100 .0 7 1 5 4
120 .06983
150 .06725
200 . 06295
10 11 12
6. 28 -11.88 12 . 00 003 11. 28 1. 78
6. 87 -13. 22 11.82 001 -12. 63 0. 89
6. 39 -12. 13 -1 5 .3 9 017 11. 53 1 . 01
TABLE C-l (Cont'dl
1 2 3 4 4a 5 5a 6 6a 7 8
9 10 11 12
#11 S ak ia d is
77 .0 8 0 6 9 56
.07485 -7. 2 .0 8 0 6 9
0. 0 .07485 -7. 2 6. 02 -11. 29 -16. 15 . 025 - 1 0 .6 9 1. 08
100 .0 7 8 6 8 .07301
120 .0 7 7 6 0 .07693 -0. 9 .07141 -8. 0
150 .07711 .07431 4. 5 .06901 -2. 9
200 .0 6 5 7 4 .0 6 9 9 4 6. 4 .06501 - 1 .1
#12 M alian
77 .0 7 7 1 6 .0 7 7 7 4 0. 8 .0 7 7 1 6 0. 0 .0 7 7 7 4 0. 8 5. 71 - 1 0 .5 8 - 1 1 .2 0 .011 -9. 98 1 .5 6
100 .0 7 5 1 8 .0 7 5 3 6 0. 2 .0 7 5 9 6 1.0
120 .0 7 3 4 3
1
.0 7 3 7 9 0. 5 .0 7 4 4 0 1. 3
150 .0 7 0 8 4 .07145 0. 9 .0 7 2 0 8 1.8
200 .06651 .0 6 7 5 4 1. 6 .0 6 8 2 0 2. 5
#13 R ie d e l
77 .08439 53 .0 8 5 0 6 0. 8 .0 8 4 3 9
0. 0 .0 8 5 0 6 0. 8 6. 68 - 1 2 .7 9 - 1 2 .7 5 . 026 - 1 2 .1 9 1. 86
100 .0 8 1 7 0
.0 8 1 9 9 0. 4 .0 8 2 6 8 1.2
120 .0 7 9 4 2 .07991
0. 6 .08060 1. 5
150 .0 7 4 9 8 .0 7 6 7 8 2. 4 .0 7 7 4 9 3. 4
200 .06881 .0 7 1 5 7 4. 0 .07231 5. 1
#14 J o b s t
77 .1 0 6 4 0 28 .1 0 4 4 4 - 1 . 8 .1 0 6 4 0 0. 0 .1 0 4 4 4 - 1 . 8 6. 60 12. 61 -1 0 .9 5 44. 3 -9 . 97 32. 9
100 .10360 .1 0 3 9 3 0. 3 . 10204 - 1 . 5
120 .1 0 1 1 7
.1 0 1 7 9 0. 6 .0 9 9 9 6 - 1 . 2
TAB LE C-l (Cont'c
1 2 3 4 4a 5 5a 6 6a
150 .09748 .09857 1. 1 .09684 -0. 7
200 .09139
.09321 2. 0 .09163 -0. 3
#15 Jobst
77 .09400 28 .09361 -0.4 .09400 0. 0 .09361 -0. 4
100 .09183 .09195 0. 1 .09160 -0. 3
120 .08998 .09017 0. 2 .08984 -0. 2
150 .08720 .08750 0. 3 .08721 0. 0
200 .08255 .08305 0. 6 .08283 0. 3
#16 Jobst
77 .08645 28 .08852 2.4 . 08645 0. 0 .08852 2. 4
100 .08503 .08499 -0. 1 .08700 2. 3
120 .08382 .08363 -0.2 .08568 2. 2
150 .08200 .08166 -0.4 .08369 2. 1
200 .07895 .07838 -0. 7 .08038 1. 8
#17 Riedel
77 .08819 53 .09001 2. 1 .08819 0. 0 .09001 2. 1
100 .08689
.08681 -0. 1 .08863 2. 0
120 .08578 .08561 -0. 2 .08743 1. 9
150 .08403 .08382 -0. 3 .08562 1. 9
200 .08120 .08082 -0. 5 .08262 1. 8
00
Malian
77 .07748 .07449 -3. 9 . 07748 0. 0 . 07449 -3. 9
6. 30 -11. 92 - 10. 68
5. 46 10. 01 6. 50
4. 94 -8. 82 -6. 50
5. 53 -10. 17 ■5. 41
10
42. 1
33. 7
68. 9
11 12
42. 7 9. 36 28. 0
7. 47 26. 5
-6. 68 22. 8
-6. 40 41. 9
TABLE C-l (Cont'd)
1 2 3 4 4a 5 5a 6 6a 7 8 9 10 11 12
100 .07655 .07633 -0. 3
.07339
-4. 1
120 .07576 .07532 -0. 6 .07244 -4. 4
150 .07449 .07382 -0. 9 .07101 -4. 7
200 N on Lin - - - -
#19
Jo b st
77 .09900 28 .09678 -2. 2 .09900 0. 0 .09678 -2. 2 9. 57 -19.38 -18.88 10. 7 -18.29 15. 7
100 .09504 .09480 -0. 2 .09271 -2.4
120 .09163 .09115 -0. 5 .08917 -2.7
150 .08660 .08568 - 1. 1 .08386 -3.2
200 .07809 .07655 -2. 0 .07501 -3. 9
#20 J o b s t
77 .09250 28 .09250 0. 0
8. 13 -13.52 20. 8 16. 5
100 .08959
.08938 -0. 2
120 .08702 .08666 -0. 4
150 .08321 .08259 -0. 8
200 .07685 .07581 -1.4
= # =
r - o
! —*
J o b s t
77 .08403 28 .08403 0. 0 7. 26 -9. 99
12. 2 12. 5
100 .08218 .08218 -0. 8
120 .08043 .07930 -1.4
150 .07792 .07600 -2. 5
200 .07373 .07050 -4.4
TABLE C-l fCont'd. )
1 2 3 4 4a 5 5a 6 6a 7 8 9 10 11 12
#22 S c h m id t
77 .09271 59 .0 9 2 9 3 -0. 2 .09271 0. 0 .09293 -0. 2 5 .2 0 -9. 42 0. 83 216. 0 1. 12 75. 2
100 .09460 .0 9 2 9 6 -1. 7 .09317 - 1 .5
120 .0 9 6 2 9 .0 9 3 1 8 -3. 3 .09338 -3. 0
150 .0 9 8 8 6 .09351 - 5 . 4 .0 9 3 6 9 - 5 .2
200 .10305 .0 9 4 0 6 -8. 7 . 09421 -8. 6
#23 R ie d e l
77 .09213 53 .0 8 2 9 9 - 9 . 9
.09213 0. 0 .0 8 2 9 9 -9. 9 8. 08 -1 5 .9 8 -14. 60 17. 1 -14. 60 16. 9
100 .0 8 9 0 0 .08901 -0. 0 .0 8 0 2 0 -9. 9
120 .08635 .08629 -0. 1 .0 7 7 7 8
-9. 9
150 .08237 .08222 -0. 2 .0 7 4 1 5 -10.
200 .0 7 5 6 9 .0 7 5 4 4 -0. 3 .0 6 8 0 9 -10.
#24 J o b s t
77 .0 8 2 8 9
28
.08069 - 2 . 7 .0 8 2 8 9
0. 0 .0 8 0 6 9 -2. 7 7. 30 -14. 20 -1 0 .3 1 55. 6 -11. 05 22. 8
100 .0 8 0 8 4 .0 8 0 7 6 -0. 1 .0 7 8 6 4 -2. 7
120 .0 7 9 0 9 .07892 -0. 2 .0 7 6 8 6 -2. 8
150 .0 7 6 4 3 .0 7 6 1 4 -0. 4 .07418 - 2 . 9
200 .07201 .07152 -0. 7 .06973 - 3 . 2
#25 P o w e ll
-- ■
77 . 3510 27 . 3526 0. 5 1. 43 -0. 82 13. 7 3 1 1 .7 13. 8 132. 9
100 . 3615
120 . 3696
150 . 3800
TABLE C-l fCont'd. )
1 2 3 4 4a 5 5a 6 6a 7 8
9 10 11 12
#26 V e n a r t
77 . 3405 27 . 3925 15. 1. 72 -1. 48 13. 6 298. 5 12. 55 147. 7
100 . 3503
120 . 3570
\
150 . 3645
200
#27 Glass m 1 n
77 .14720 18 . 15320 4. 1 .1 4 7 2 0 0. 0 . 15320 4. 1 3. 02 -4. 45 2. 52 1 26.2 1. 96 72. 8
100 . 14873 .1 4 7 8 6 -0. 6 . 15389 3. 5
120 .15002
.1 4 8 4 3 -1. 1 .1 5 4 4 9 3. 0
150 .1 5 2 0 2
.1 4 9 2 8 - 1 . 8
.1 5 5 3 9 2. 2
200 .15531 .15071 -3. 0 .1 5 6 8 9
1.0
#28 M alian
77 .1 1 5 9 0 . 12475 7. 6 .1 1 5 9 0 0. 0 .1 2 4 7 5 7. 6 3. 93 -6. 52 0. 59 130. 4 0. 08 67. 8
100 .1 1 5 4 0 .11588 0. 4 .1 2 4 7 3 8. 1
120
.11491 .1 1 5 8 9 0. 8 .12471 8. 5
150 .11422 .1 1 5 8 6
1. 4 .12468 9 .2 !
200 .1 1 3 0 7 .1 1 5 8 3 2. 4 .1 2 4 6 3 9 . 3 ,
#29 M aso n
77 .1 7 0 6 5 36 .15921 -6. 7 .1 7 0 6 5 0. 0 .15921 -6. 7 2 .8 7 -4. 10 3.'96 167. 3 4. 19 104. 5
100 .1 7 2 1 9 .1 7 1 6 4 -0. 3 . 16074 -6. 6
120 .1 7 3 5 6 .17307 r0. 3 .1 6 2 0 8 -6. 6
150 . 17552 .1 7 5 2 2 -0. 2 .16908 - 6 . 5
200 . 17887
.1 7 8 7 9 -0. 1 .16742 -6. 4
1 — 1
4*
00
TABLE C-l fCont'd. )
1 2 3 4 4a 5 5a 6 6a 7 8
9
10 11
#30 Malian
77 .07878 .07878 0. 0 6. 21 -11. 72 -12. 11 -11.8 -12.07
100 .07660 .07664 0. 1
120 .07465 .07477 0. 2
150 .07182 .07198 0. 2
200 .06705 .06732 0. 4
#31 Malian
77 .08543 .08079 -5. 4 .08543 0. 0
.08079
-5.4 4.60
LD
O
00
1
-8. 31 -43. 3 -9. 44
100 .08380 .08354 -0. 3 .07904 -5. 7
120 .08238 .08189 -0. 6 .07741 -5. 9
150 .08026 .07942 -1. 0 .07522 -6. 3
200 .07672 .07531 -1. 8 .07141 -6.9
#32 Malian
77 .08047 .08047 0. 0 4. 64 -8. 14 -7. 44
8. 7 -10, 24
100 .07908 .07860 -0. 6
120 .07788 .07698 -1.2
150 .07608 .07454 -2. 0
200 .07308 .07048 -3. 6
#33 Malian
77 .08608 .09257 7. 6 .08608 0. 0 .09257 7. 6 5. 04 -9. 05 -9. 36
• ' f
o
1
-4. 02
100 .08442 .08527 1.0 .09174 8. 7
120 .08321 .08457 1. 6 .09099 9. 4
150
.08039 .08352 3. 9 .08987 11.
299
.07672 .08176 6. 6 .08861 15,
TABLE C-l fCont'd.)
1 2 3 4 4a 5 5a 6 6a
#34 M alian
77 .0 5 8 0 3 .07121 23- .05803 0. 0 .07121 23.
100 .0 5 6 5 4 .0 5 6 3 6 -0. 2 .0 6 9 1 8 22.
120 .0 5 5 1 2 .0 5 4 9 0 -0. 4 .06742 22.
150 .0 5 3 0 4 .05272 -0. 6 .0 6 4 7 8 ZZ
200 .0 4 9 6 3 .0 4 9 0 9 -1. 1 .0 6 0 3 7 ZZ
#35 J a m e s o n
77 .0 6 8 2 6 27 .0 6 8 5 3 0. 4 .0 6 8 2 6 0. 0 .0 6 8 5 3 0. 4
100 .0 6 7 4 9 .0 6 6 8 3 -1. 0 .0 6 7 1 2 -0. 6
120 .0 6 6 8 2 .0 6 5 5 9 -1. 8 .0 6 5 8 9 -1. 4
150 .06582 .06372 -3. 2 .0 6 4 0 5 - 2 . 7
200 .0 6 4 1 5 .06061 -5. 5 .0 6 0 9 7 -5. 0
#36 R ie d e l
77 .05820 53 .0 7 8 6 0 36. .0 5 8 2 0 0. 0 .0 7 8 6 0 36.
100 .0 5 7 1 8 .05711 -0. 1 .0 7 7 1 6 35.
120 .0 5 6 3 6 .0 5 6 1 7 -0. 3
.07591
35.
150 .0 5 5 0 6 .05475 -0. 6 .07402 34.
200 .05293 .0 5 2 3 8 -1.0
.0 7 0 8 9 34.
#37 R ie d e l
77 .0 6 4 0 4 53 .07402 16. .0 6 4 0 4 0. 0 .07402 16.
100 .0 6 2 5 6 .0 6 2 8 0 0. 4 .07261 16.
120 .06125 .0 6 1 7 2 0. 8 .0 7 1 3 9 17.
150 .0 5 9 3 8 .06011 1 .2 .0 6 9 5 5 17.
200 .05617 . 05741 2. 2 .0 6 6 4 9 18.
10 11 12
6. 76 -12. 97 - 1 3 .1 9 0. 05 -12. 37 5. 94
5. 29 -9 . 62 -4 . 75 1 . 22 ■8. 97 14. 57
4. 84 -8. 59 -7. 04 0. 48 -7. 96 11. 50
5. 00 -8. 96 -9. 93
2. 03 -8. 29 18. 25
c_n
O
1
#38
77
100
120
150
200
#39
77
100
120
150
200
#40
77
100
120
150
200
#41
77
100
120
150
200
4 4a 5 5a 6 6a 7 8 9 10 11 \ l 2
.04998 3. 1 .0 5 1 5 6
.0 5 0 1 6
.04895
.04712
.09408
0. 0 .04998
.0 4 8 6 4
.04748
.0 4 5 7 4
.04283
3. 9 6. 50 -1 2 .3 8 - 3. 19 -11. 64 38. 2
.0 4 8 1 9 -19 .0 5 9 5 3
.05753
.0 5 5 7 9
.05318
.04883
0. 0 .04819
.0 4 6 5 9
.0 4 5 1 9
.04310
.03961
-19- 7. 75 - 1 5 .2 3 3. 51 - 1 4 .4 7 25. 8
.0 7 8 2 6 1.3 .07728
.0 7 5 2 4
.07347
.07081
.06638
0. 0
-0. 5
-1. 0
-1. 9
-3. 4
.0 7 8 2 6
.07622
.07445
.0 7 1 8 0
1..3
0. 8
0. 3
-0. 6
6. 46 - 1 2 .2 9 -8. 82 8. 13 -1 1 .3 2 22. 4
.07175 8. 0 .06645
.06468
.0 6 3 1 6
.06087
.05707
0. 0
0. 0
0. 0
0. 1
0. 2
.07175
.06988
.0 6 8 2 6
.06583
.06178
8. 0
8. 1
8. 1
8. 3
8. 5
6. 30 -11. 92 -11. 12 0. 51 - 11. 30 10. 10
( — >
C n
1 2 3 4 4a 5 5a 6 6a
#42 M alian
77 .0 6 2 2 2 .0 8 3 1 0 34. .0 6 2 2 2 0. 0 .0 8 3 1 0 34.
100 . 06097 .06061 -0. 6 .08121 34.
120 .0 5 9 2 3 .0 5 9 3 6 0. 2 .07951 34.
150 .0 5 7 1 8
.0 5 7 4 9 0. 5 .0 7 7 1 0 35.
200 .0 5 3 7 0 .05438 1. 3 .0 7 3 0 0 36.
#43 J o b s t
77 0. 1286 28 0.1311 1- 9
CARBOXYL.IC ACIDS
100
120
150
200
#44 J o b s t
77 0. 09242 28 0 .1 3 1 8 8 29. 9
C O U L D N OT
100
120 BE
150
200
#45 J o b s t
77 0. 08011 28 0 .1 3 6 3 0 41. 2 C O R R E L A T E D
100
120
150
5. 67
- 1 0 .4 9 -10. 74
10
0. 09
11
-9. 89
12
6. 65
5. 66 10. 33 11 . 88 -135 10. 47 37. 2
6. 00 11. 24 6, 86 -3. 73 11. 25 5. 92
5. 75 10. 65 4. 56 0. 50 10 . 66 4. 33
t - 1
cn
OJ
T A B L E C - l (C o n t'd .)
E x p e r i m e n t a l D ata on P e t r o l e u m M ix tu re s
No. N a m e
k ex p t'l.
B t u / h r ft ° F
R ef.
T h e r m .
Cond.
D e n s ity
l b / f t 3
P
H e a t
C a p a c ity
B tu /lb ° F
s
V is c o s ity
C ps
T 1
D en.
Coef.
°jr~ 1
a x 104
C ond.
Coef.
V 1
X X 104
Mol.
Wt.
51 D u P o n t Oil
M alian 388
77 0 .0 8 4 2 2 54. 9 42. 1 215 3. 86 -5. 13
100 0 .0 8 3 2 2 54. 4 43. 8 105
120 0 .0 8 2 3 7 54. 0 45. 2 57
150 0 .0 8 1 0 8 53. 4 47. 7 29
200 0 .0 7 8 9 0 52. 3 52. 7 12
52 G ulf H a rm o n y
#204 M alian 400
77 0. 09188 55. 6 40. 7 2200 3. 62 -4. 36
100 0 .0 9 0 9 2 55. 2 44. 3 940
120 0 .0 9 0 1 2 54. 9 45. 6 460
150 0 .08895 54. 3 47. 4 205
200 0 .0 8 6 9 6 53. 2 48. 4 54
53 C h e v ro n A lta
V is 530 M alian 452
77 0 .0 6 6 7 4 54. 5 40. 2 11300 3. 29 -0. 36
100 0. 06669 54. 1 42. 7 4450
w
TABLE C-l (Cont'd.)
No. N a m e
k e x p t'l.
3 tu /h r ft ° F
R ef.
T h e r m .
Cond.
D e n s ity
l b / f t 3
P
H e a t
C a p a c ity
B tu / lb ° F
c p
V is c o s ity
C p s
1 1
Den.
Coef.
O p - 1
a x 104
Cond.
Coef.
O p - 1
X x 104
Mol.
Wt.
120 0 .06662 53. 8 0. 445 1820 3. 29 -0. 36
150 0.06657 53. 2 0. 468 510
200 0.06645 52. 4 0. 497 120
54 G ulf O il #896 M alian 178
77 0. 07780 50. 9 0. 426 4. 4 4. 50 - 7 .7 5
100 0.07641 50. 4 0. 444 3. 1
120 0 .07520 50. 0 0. 462 2. 3
150
0 .0 7 3 3 9 49. 2 0. 488 1.7
200 0. 07039 48. 2 0. 520 1. 1
55 S h ell P r e m . D i e s e l M alian 176
77 0 .0 7 2 1 8 50. 6 0. 412 1. 85 4. 95 -8. 59
100 0 .0 7 0 7 3 49. 8 0. 429 ■ 1. 47
120 0.06 9 4 8 49. 4 0. 447 1.22
150 0. 06763 48. 8 0. 473 0. 92
200 0. 06456 47. 5 0. 504 0. 64
TABLE C-l (Cont'd. )
H e a t Den. C ond.
R ef. D e n s ity C a p a c ity V is c o s ity Coef. Coef.
k e x p t'l. T h e r m . l b / f t 3 B tu / lb ° F
C p s
o F - l ° P - 1
Mol.
No. N a m e B t u / h r ft ° F Cond.
P
C P
a x 10^ X x 104 Wt.
56 C h e v r o n D ie s e l
F uel M a lia n
77 0. 07203 53. 1 0. 400 3. 9 4. 43 -7. 54
100 0 .0 7 0 7 7 52. 5 0. 423 2. 9
120 0 .0 6 9 6 8 52. 0 0. 441 2. 2
150 0 .0 6 8 0 6 5 1 .2 0. 464 1. 6
200 0 .0 6 5 3 7 50. 0 0. 484 1 .0
156
APPENDIX D
PHYSICAL PROPERTIES REQUIRED FOR THE
PREDICTION OF k AND dk/dt
Table 1 presents literature values for:
1) Cp - heat capacity of the liquid at
77° F Btu/lb ° F
2) p - density of the liquid at 77° F,
lb /ft3
m
3) Tc - critical temperature of the liquid, 0 R
4) M - molecular weight of the liquid
5) AS* - normal boiling point entropy of
vaporization as calculated by Everett’s
Method from latent heat of vaporiza
tion data
6) y - dipole moment of the molecules com
prising the liquid
7) - dielectric constant of the liquid at
77° F.
Table 2 presents literature references for the
above physical properties. For the most part, reliance
was placed upon the single source reference compilation
edited by Weissberger £t a_l. (70) . For the few instances
where a physical property was listed by Weissberger et^
al, but a different value was chosen, this value was
referenced by the notation W/#. References without W
indicate the value was not listed in the compilation o
Weissberger.
ICT denotes data taken from the "International
Critical Tables," McGraw-Hill, New York, 1926.
APPENDIX D
T A B L E D- 1
P h y s i c a l P r o p e r t i e s of the L iq u id s a t 7 7 ° F
( R e f e r e n c e s a r e given in A ppendix D -2)
Liq.
No.
D en sity
P
l b / f t 3
H e a t
C a p a c ity
Cp
B t u / l b ° F
Mol.
Wt.
M
C r it .
T e m p .
T c
°R
H e a t of
Vap.
A H
B tu / lb m o
, Boil.
P t.
T b
. °R
E n t. of
V ap.
A S*
B tu / l b moL F
D ipole
M om .
V >
e. u.
D ie le c t.
C o n s ta n t
1
39. 1 0. 560 72. 1 846 11, 088 557 19. 66 0. 00 1. 84
2 4 6 .2 0. 435 70. 1 921 11, 743 581
19.89 0. 00 1. 96
3 40. 9 0. 541 86. 2 914 12, 413 616 19. 70 0. 00
1. 89
4 46. 0 0. 442 84. 2 996 12, 942 637 19. 81 0. 00 2. 02
5 40. 4 0. 538 86. 2 897 11, 957 601 19. 50 0. 00 1. 98
6 41. 0 0. 522 86. 2 901 11, 734 596 19. 31 0. 00 2. 00
7 46. 4 0. 451 84. 2 960 12, 449 621 19. 58 0. 00 1. 98
8 47. 7 0. 443 98. 2 1030 13, 644 674 19. 62 0. 00 2. 02
9 42. 4 0. 532 100. 2 973 13,635 669 19. 72 0. 00 1. 92
10 43. 6 0. 525 114. 2 1025 15, 648 718 20. 21 0. 00 1. 95
11 44. 5 0. 524 128. 2 1072 16, 254 763 20. 43 0. 00 1. 97
12 46. 7 0. 529 142. 9 1087 16, 902 805 20. 02 0. 00
1- 99
13 54. 5 0.411 78. 1 1011 13, 235 636 20. 30 0. 00 2. 28
14
49. 1 0. 590 32. 0 924 15,156 608 24. 50 1. 66 32. 6
15 49. 0 0. 590 46. 1 927 16, 747 633 26. 00 1. 67 24. 3
TABLE D-l (Cont'd)
Liq.
No.
D e n s ity
P ,
lb /f t
H e a t
C a p a c ity
P n
B tu / lb F
Mol.
Wt.
M
C r i t .
T e m p .
T
- 1 c
OR
H e a t of
Vap.
A H
B tu / lb m o
B oil.
P t.
Tb
1. °R
E n t. of
Vap
a s’
B tu / lb m o l.° .
D ipole
M om .
M -
- e. u.
D ielect.
C o n s ta n t
16 49. 9 0. 570 60. 1 967 17, 790 667 26. 07 , 1. 75 2 1 .8
17 50. 3 0. 571 74. 1
1009 19, 345 704 26. 78 1 1.81 17. 1
18 60. 0 0. 452 100. 2 1126 21, 000 782 26. 08 1. 90 15. 0
19
48. 1 0. 520 44. 0 986 11, 061 528 20. 80 2 .4 9 21. 1
20 49. 9
- 58. 1 (952) 12,880 578 21. 95 2. 73 18. 5
21 49. 7
- 72. 1 (1023) 13, 940 627 21. 77 2. 72 13. 4
22 72. 0 0. 416 96. 1 1253 16, 600 782 20. 29 3. 61 40. 0
23 49. 0 0. 531 58. 1 92 0 12,766 593 21. 26 2. 72 20. 7
24 49. 9 0. 555 72. 1 960 16, 420 633 25. 44 2 . 7 4 18. 5
25 62. 2 0. 998 18. 0 1169 17, 460 672 25. 36 1. 85 78. 5
26 69. 1 1. 005 20. 0 1162 17, 890 674 24. 04 2. 04 78. 2
27 69. 3 0. 581 62. 1 (1204) 21, 353 847 24. 13 2. 28 37. 0
28 64. 4 0. 593 76. 1 (1180) 23, 220 831 26. 90 2. 00 32. 0
29
78. 5 0, 580 92. 1 (1348) 25, 620 1014 23. 83 2 .2 5 42. 5
30 61. 4 -
89. 1 1113 15, 030 708 19. 31 3. 76 25. 5
31 74. 8 0. 344 123. 1 1342 17, 539 872 18. 98 3. 79 34. 8
32 71. 7
- 137. 1 - 20, 248 909 21. 00 4. 25 23. 8
33 62. 6 0. 440 103. 1 1259 17, 259 836 19. 42 4. 05 25. 2
34 98. 7 0. 207 153. 8 1001 12,890 630 20. 12 0. 00 2. 24
35 92. 2 0. 231 119. 4 965 12, 636 602 20. 78 1. 15 4. 81
36 113. 8 0. 186 204. 0 1298 17, 411 831 19. 91 1. 70 4. 63
TABLE D-l (Cont'd)
L i q .
No.
D e n sity
P
l b / f t 3
H e a t
C a p a c ity
C P
B tu /lb F
Mol.
Wt.
M
C r it .
T e m p .
T c
OR
H e a t of
V ap.
A H
B tu /lb m o
Boil.
P t.
Tb
1. ° R I
E n t. of
Vap.
A S'"
itu /lb m o l. °.
Dipole
M om.
V
? e. u.
D ielect.
C o n sta n t
37 92. 9 0. 221 157. 0 1208 16, 288 111 21. 10 1. 73 5. 40
38 120. 1 0. 176 156. 0 998 12,809 622 20. 34 1. 78 7. 82
39
90. 5 0 .2 1 0 109. 0 917 11, 502 561 20. 50 2. 01 9. 39
40 77. 7 0. 312 99. 0 1011 13, 777 642 21. 19 2. 06 10. 36
41
91. 1 0 .2 2 3 131. 4 (1038) 14, 938 649 20. 59 0, 90 3.4 2
42 100. 8 0. 216 165. 8 1117 13, 538 710 20. 67 0. 00 2. 30
43 75. 6 0. 550 46. 0
-
9, 972 673 14.26 1. 19 58. 5
44 65. 1 0. 490 60. 1 959 10, 485 704 14. 18 0. 83 6. 15
45 59. 4 - 88. 1 1296 18, 072 786 22, 06 0. 65 2. 97
N otes: (1) A S* = ^ ( R i n ) ( E v e r e t t 's E n tro p y of V a p a riz a tio n ) (15)
Th K 1 T b
(2) T c V a lu e s in ( ) a r e e s ti m a t e d f r o m boiling pt. by L y d e r s o n 's M ethod (51)
TABLE D-2
R e f e r e n c e s fo r P h y s i c a l P r o p e r t i e s
L iq .
No. D e n s ity
H e a t
C a p a c ity M ol. Wt.
E n tr o p y
V a p o r .
D ipole
M o m .
D ie le c .
C o n s ta n t
1 W W W W W W
2 W W W W W W
3 W W w W W W
4 W W w W W W
5 W W w W W W
6 W W w W W W
7 W W w W W W
8 W W w W W W
9 W W w W W W
10 W W w W W W
11 W W w W W W
12 W W w W W
. w
13 W W w W W W
14 W W w W W W
15 W W w W W W
16 W W w W W W
17 W W w W W W
18 W W w W /4 0 W w .
19 W W
w ICT W
W
20 W - w ICT W W
21 W -
w ICT W W
22 W w w W W W
23 w w w W W W
24 w w w W W W
25 ICT IC T ICT ICT 37 IC T
26 31 31 31 31 37 31
27 W W w W / 12 W W
28 W W
w W / 12 W
W
29 W
W w W /4 4 W /3 7 w
30 W -
w W /2 0 W w
31 W w w W W w
32 4 -
4 4 37 35
33 W /IC T w
w W / ICT W W
34 W w w W W ' W
35 W w w
W W W
36 W w w W W W
37 W w w W W W
38 W w w W W W
39 W w w W W W
40 W w w W W W
41 W w w W W W
42 w w w W W W
162
APPENDIX E
OUTLINE OF TRIAL-AND-ERROR PROCESS FOR OBTAINING
CORRELATIONS $ AND 0 FOR THE DEVIATIONS
OF POLAR LIQUIDS
1) Process for the Correlation Group $
The correlation group $ was intended to correlate
the deviation of polar liquids from the thermal conduc
tivity values predicted at 77° F by a modified form of
the Weber Equation, Eq. IV-3 of this dissertation.
The thermal conductivity deviation was expressed
as Ak where:
Ak = 0.00433 p C
T > 1/3
c
p 1000 M
- k expt'l. Btu/hr ft °F
The intended correlation was to be of the form Ak a $
where $ was to consist of various permutations of the
following parameters:
a) AS*/19.7, normal boiling point entropy of
vaporization ratio
b) u, dipole moment of the molecules comprising
the liquid
c) e, dielectric constant of the liquid at 77° F
d) P/P^ o ’ density ratio at 77° F
2
163
The above correlating parameters were evaluated
in the following classes of groups:
b
I)
II)
f AS* 1
a
* -
P
19. 7
V J
L pH-,0
Cue)
a = 1, 2, 3 )
b = 0, 1, 2, 3 ) 8 permutations
c = 1
)
AS*
a
f \
P
19.7
L pH70
(U + e)
a = 1, 2, 3, 4
)
b = 1, 2, 3, 1.2, 1.4, 1.6, 1.8 )
c = 1/2, 1
)
18 permutations
HI)
IV)
f A S *
a
r \
P
19.7
\ J
^ PH^0 >
a = 1 )
b = 1.2 )
c = 1.4 )
)
a = 1
b = 1.2 )
c = 1.4 )
(1 + ye)'
[ AS*
a
f -V
p
19.7 J ^ P tt n
1 permutation
b
(1 + ye)
1 permutation
V)
AS*
19. 7
Ph2°J
a = 1 )
b = 0 )
c = 1/2, 1, 2 )
d = 1/2, 1, 2 )
(y) Ce)
12 permutations
The correlating group 4 was evaluated for all of
the above 35 permutations. For the better permutations,
Ak vs. $ data were plotted and if the visual results
164
looked promising, a least square regression analysis was
performed. On the basis of Standard Error of Estimate*
resulting from the regression analysis, the final per
mutation was chosen from Class II such that
Aka
( AS*
' 19.7
2
ph2o
2
(y + e)
The proportionality constant was evaluated by
least square regression analysis as 0.00088 and the
standard error of estimate was calculated as
+ 4.77 x 10"3 Btu/hr ft ° F
2) Process for the Correlation Group, 0
The correlation group 0 Was intended to correlate
the deviation of polar liquids from the theoretical tem
perature dependency of thermal conductivity as predicted
at 77° F by the Horrocks and McLaughlin Relationship.
The temperature dependency of thermal conductivity
deviation was expressed as AA where
" ^Horrocks-McLaughlin ^expt'l., in Btu/hrft °F^
Note: Au „ = -0.000244 + 2.28 — ---
H-M p dt
A 1 dk
expt'l. ~ k dt
Standard Error of Estimate = S = I ^ (7 . ycalc^ _
xy V n
165
The intended correlation was to be of the form
AAa0 where 6 was to consist of various permutations
of the following parameters:
a) AS*/19.7, normal boiling point entropy of
vaporization ratio
b) y, dipole moment of the molecules comprising
the liquid
e) e, dielectric constant of the liquid at 77° F
The above parameters were evaluated in the follow
ing classes of groups:
■ hi b
I)
AS*
19.7 J
2°
(y + e)
a = 1, 2 )
b = 0, 1, 2 ) 12 permutations
c = 1/2, 1 )
II)
f AS*
a
• i
P
19.7 j
Oh 20 J
1 + (ye)
)
a = 2
b =-0, 1, 2 ) 14 permutations
c = 1/4, 1/3, 1/2, 1 )
Ilia)
AS* . '
a
f
P
19.7 i J
pH20 J
a = 1/2, 1
b = 0, 1, 1
2, 1.4, 2
(1 + ye)
)
) 17 permutations
c = 1, 1.1, 1.2, 1.3, 1.4, 1.5 )
166
m b )
IIIc)
f AS* J
a ( \
P
19.7
1 ph2o
a = l
)
3 = 1, 1.2, 1.4 ) 2
; = 1
)
f A S * - ll
» «
P
[ 19.7 ,
L pH.O
C4 + ye)
(10 + ye )u
a = 1/2, 1 )
b = 1.2 ) 8 permutations
c = 1, 1.1, 1.2, 1.3, 1.4, 2 )
The correlating group 0 was evaluated for all of
the above 51 permutations. For the better permutations,
AAvs. 0 data were plotted and if the visual results
looked promising a least square regression analysis was
performed. On the basis of the Standard Error of Estimate
(6AA) , the final permutation was chosen from Class Ilia
such that
1 . 2
AA a A - 1
r P
19.7
^pH.O
(1 + ye)
1.4
The slope and intercept was found by regression
analysis to be (0.447 + 0.047 0) x 10"4 Btu/hr ft ° F2.
The standard error of estimate was found to be:
SAX = + 1.16 x 10"5 Btu/hr ft ° F2
A summary of the class evaluations for the standard
error of estimate was found to be as follows:
167
Class Evaluation of Correlations for AX vs. 0
(Note: SAk are given as Btu/hr ft ° x 105)
I) Poor
Considerable difference alcohols and other
liquids at low AX, Nitrile and Nitrates
very poor.
Best results when a = 1
b = 2
c = 1
II) Very poor, except when Hv. Liqs. are excluded,
then moderate at best.
Ilia) Moderate at best when c = 1
<5AX varies at best from 1.45 0 a = 1
b = 2
c - 1
to 1.710 a = 1
b = 0
c = 1
Ilia) (cont.)
Good when c > 1
varies from 1.47 to 1.16
a = 1, = 1
b = 1, » 1.2
c = 1, =-1.5
Illb) 6AX 0 1.47
IIIc) SAX 0 1.58 to 1.18
a = 1, = 1
b = 1.2, = 1.2
c = 1, = 1.4
168
APPENDIX F
DEGREE OF MOLECULAR ASSOCIATION OF SOME LIQUIDS
AS A FUNCTION OF TEMPERATURE
The molecular association of some liquids is
apparently independent of temperature while for others
the degree of association is temperature dependent.
The ramifications of this have been discussed in
Chapter VI, Section A.
Most of the data concerning the degree of associ
ation as a function of temperature have been reported by
Thomas (64, 6S). A summary of his data concerning the
consistency of the association of the first ten alcohols
is presented in Table F-l.
An extension of this work by Thomas reveals that
not all liquids possess constant degrees of molecular
association. The results of this work are presented
in Table F-2.
Of the seventeen liquids tabulated in Table F-2,
sufficiently accurate thermal conductivity data were
available only for m-Cresol. Using the data of Thomas,
an attempt was made to estimate the degree of molecular
169
association, , of this liquid at 77° F. The results are
given in Table F-3 and Figure F-l.
TABLE F-l
ALCOHOLS OF CONSTANT MOLECULAR ASSOCIATION AS REPORTED
BY L. H. THOMAS, J. CHEM. SOC., 1948, 1345
Alcohol Mo1, Temp. Range
Investigated As=oc‘ Investigated
Methanol 1.44 0 - 60
Ethanol 1.91 0 - 70
Propanol 2. 33 0 - 90
iso- propanol 2.87 0 - 80
Butanol 2.21 0 - 100
iso-Butanol 2. 74 10 - 100
iso- Amyl 2.21 10 - 130
n-Hexanol 2.17 35 - 155
n-Heptanol 1.75 40 - 140
n-Octanol 1.87 20 - 100
TABLE F-2
170
M o l e c u l a r A s s o c i a ti o n v s . T e m p e r a t u r e D ata a s R e p o r t e d
by L. H . T h o m a s , J . C h e m . Soc. (L o n .) I960, 4906
S u b sta n c e
In v e s tig a t e d
V a lu e s of Y a t v a p o r p r e s s u r e s :
760 250 100 40 10 3
P h e n o l 1. 52 1. 62 1.71 1. 78
1. 89 1. 99
O - C r e s o l 1. 42 1 .5 3 1. 65 1. 76 1. 95 -
M - C r e s o l 1. 53 1. 63 1. 72 1. 80 1. 92 2. 03
p - C r e s o l 1. 48 1. 61 1. 72 1. 83 2. 01 2. 15
p - C h l o r o p h e n o l 1, 47 1 '■ ■ * » c o n s t a n t
o - C h lo r o p h e n o l 1. 31 1. 39 1. 37 1. 40 1. 44 1. 48
o -M e th o x y p h e n o l 1. 27 1. 30 1. 33 1. 36 1. 39 -
m - M e t h o x y -
phenol 1. 48 1.51 1. 54 1. 57 1.61 -
p -M e th o x y -
phenol 1. 52 1 .5 6 1. 59 1. 62 1 .6 6 -
M ethyl p - h y -
d r o x y b e n z o a te - 1. 60 1. 61 1. 63 1 .6 6 1. 69
M ethyl
S a lic y la te 0
1
o
o
n s 1 a n t
o - N itr o p h e n o l 1.17 —^ c o n s t a n t
o -H y d r o x y a c e to -
phenone 1.13 — « * ■ c o n s t a n t
S a lic y la ld e h y d e 1.13 —•• c o n s t a n t
A c e ta m id e 1. 42 1.51 [ 1. 60 1 .6 8 1 1. 80
-
P r o p i o n a m i d e 1. 55 1. 61 1 1. 66 1 1. 70 1 1. 77 1. 84
n - B u ty r a m i d e 1. 85 — c o n s t a n t
1 1 •
TABLE F-3
171
D e g r e e of M o le c u l a r A s s o c ia tio n of m - C r e s o l v s . T e m p e r a t u r e
V a p o r v D e g r e e o
P r e s s u r e T e m p . A s s o c i a t
m m Hg °C
" Y
1 52. 0
3 (Int. ) 68. 0 (I) 2. 03
5 76. 0
10 87. 8 1. 92
20 101. 4
40 116. 0 1. 80
60 125. 8
100 138. 0 1. 72
200 157. 3
250 (Int. ) 164. 0 (I) 1. 63
400
179. 0
760 202. 8 1 .5 3
N o te : M . P . = 10. 9°C
* V a p o r P r e s s u r e v s . T e m p e r a t u r e D a ta f r o m
P e r r y ' s H andbook.
V a p o r P r e s s u r e v s . D e g r e e of A s s o c i a ti o n
f r o m R ef. (65)
-MJ4
r f e i S l . - j i i :
Lf-
( t gf t i l t K t : i &i
U j Q i t i t 5 1 1 3 . JS C :
rrr t i t t i
zrr?±n+
i: rlSSn
itSt$t±t
i&SS
■feiiiiiilii
125 150
TE M PER A TU R E
FIGURE F - l
DEGREE OF M OLECULAR ASSOCIATION OF m -C R E S O L
172
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174
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Asset Metadata

Creator Mallan, George Martin (author)

Core Title Thermal Conductivity Of Liquids

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Philosophy

Degree Program Chemical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, chemical,oai:digitallibrary.usc.edu:usctheses,OAI-PMH Harvest

Format dissertations (aat)

Language English

Advisor Lockhart, Frank J. (committee chair), Mannes, Robert L. (committee member), Rebert, Charles J. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-623981

Unique identifier UC11361985

Identifier 6813581.pdf (filename),usctheses-c18-623981 (legacy record id)

Legacy Identifier 6813581.pdf

Dmrecord 623981

Document Type Dissertation

Format dissertations (aat)

Rights Mallan, George Martin

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA