THERMODYNAMICS J. M. SMITH
AND
C. 0.BENNETT
Purdue Universify, Lafayeffe, Ind.
HE year 1955 w a s particularly important from a thermodynamic standpoint because of the June conference a t Pennsylvania State University. This meeting wm sponsored by the National Science Foundation and American Society for Engineering Education and was held June 27 to 29, a period which coincided nrith the Chemical Engineering Summer School held also a t Pennsylvania State University. The objective of the conference was to present certain aspects of thermodynamics that are having a pronounced effect on engineering and engineering education. The papers given were as follows:
T
An especially large number of books appeared during the year. Tcxtbooks included those by Belakon ( I A ) , Johnston (6A), Lee and Sears (?A), Mooney (9A), Norris (IOA), and Sweigert and Goglia (17A). A German book by Zeise (18A) is conccrned with the relationship between thermodynamics and quantum theory. Rossini’s latest book ( I 6 A )presents an analysis of n7hat is known about the properties of materials and their interrelationships. A review of classical thermodynamics, particularly the concepts upon which the first and second laws are based, is given by Finck (3A)).
‘LApplications of Thermodynamics in Distillation Calculations,” Wayne C. Edmister; “Heat Engine Applications of Thermodynamics,” C h a p y m .J. Walker; “Thermodynamics for All Engineering Students, George A. Hawkins. “Thermodynamics and Irreversible Processes,” Newman A. $all; “Irreversible Coupled,Rows,” Joseph H. Keenan; “Electric and Magnetic Phenomena, Mark W. Zemansky; “Electrochemical As ects of Thermodynamics,” Samuel Glasstone; “Statistical ,,’fhermodynamics,” R. Byron Bird; “Relaxation Phenomena,, Karl F. Heyfeld; and “Rate Processes,” Louis S. Kassel.
THERMODYNAMIC PROPERTIES
These papers are being published together and may be obtained from W. E. Rans, Pennsylvania State University. The following review is arranged in four divisions, General, Thermodynamic Properties, Phase Equilibria, and Chemical Equilibria. The survey applies to publications in 1955 and those in 1954 not included in last year’e review ( X A ) . GENERAL ARTICLES, BOOKS
The literature on irreversible thermodynamics is turning toward chemical processes. Reik ( 1 6 A ) has considered from a theoretical point of view coupled processes such as energy transfer and mass transfer in a single gas and energy transfer combined with chemical reactions. Chemical kinetics has been analyzed using the reciprocal rclations of Onsager in a general way, by Peneloux ( I d A ) , and specifically by Papov ( 1 1 A ) for the dissociation of hydrogen iodide. One of the most understandable texts on irreversible thermodynamics has been written by Prigogine ( I J A ) . The presentation is short and particularly good for chemists and chemical engineers since the equations are developed with application to chemical processes in mind. Interesting re-examinations of Sadi Carnot’s developments have becn made in the light of modern concepts. It is concluded (4.4 6 A ) that while his concept of heat as a property of a body is incorrect, his reasoning was sound and the conclusions regarding the efficiencies of heat engines were not obtained fortuitously. MacRae ( 8 A), interested in problems in teaching thermodynamics, has proposed a development of heat and entropy baaed upon regarding temperature primarily as a thermodynamic potential. Several papers appeared during the year explaining and utilizing diffusion with tagged atoms as a device for measuring vapor pressures. Priselkov and Nesmeyanov (14A ) determined vapor pressures of calcium and strontium hy measuring Knudsen diffusion of isotopes of these metals. 676
Equations of State. The problem of predicting the P-V-T behavior of gases and liquids has been the object of intensive study during the past year. The initiative for this work haa come largely from the theoretical deveIopments relating the constanta in the virial equation of state to the equations used to express the energy of interaction between molecules. From an engineering standpoint, the investigations have been confined to finding the most desirable third parameter t o add to reduced temperature and pressure a8 a means of correlating volumetric data. For spherical, nonassociating molecules with no dipole moment, tho correlation of compressibility factors in terms of reduced temperature and pressure alone has been satisfactory. When these rpstrictions are not met, several parametcrs have been used t o measure the combined effccts of deviations from sphericity, nonassociation, and charge distribution. Riedel (4Il3, 4XR) has proposed the slope of the vapor pressure curve a t the critical point, cyc, defined in the following way : =
T. (;$) Pc
c
Pitzer (QOR) suggested the slope of the vapor pressure curve a t a reduced temperature of 0.7 aR a suitable parameter. The compressibility factor a t the critical point Z,,
z,= PCV, R Tc has been known to vary from about 0.20 to 0.30 when a wide range of substances are considered. Yet for the compressibility factor to be a function of only TRand PRit should be a constant. Hence the use of 2, a8 a third parameter, originally suggested by Meissner and Sefarian in 1954 [Chem. Eng. Progr. 47, 579 (1954)], is a logical one. Lyderscn, Greenkorn, and IIougen (!39B) have reccntly prepared tables of the compressibiIity factors as a function of ?‘E, PR, and 2,and obtained good results. Using experimental data for 82 compounds for checking the tables, an average deviation of 2.5% is found for the gaseous region. For less severe conditions, the agreement is better. For the liquid phase, the average deviation i s 3.0%. Using the compressibility tables, fugacities, phase cquilibrium constants, and the effect of pressure on enthalpy, entropy and heat capacity are computed on a gencralized reduced basis.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 3
THERMODYNAMICS The agreement of the enthalpy results with experimental results is not so good as for compressibilities. Deviations of as much a8 10% are observed for isobutane. For substances that may associate such as methanol, comparison of the results with new data indicates a n average deviation of 20%. A generalized chart of compressibility factors for nonpolar gases has been developed in terms of the two constants in the LennardJones potential energy equation by Nelson and Obert (d@). The disadvantage with this approach is that it is limited to a very few substances. I n general, it is not so satisfactory as the conventional correlation in terms of T s and Pa. A new equation of state has been proposed by Martin and Hou ( S I R ) ,which takes the folloving form:
(3) where the f values are functions of temperature. The authors have developed methods of evaluating the nine constants involved in the five f pararncters from the minimum amount of experimental data. Thus, the constants can be calculated from the critical temperature, pressure, and volume and one additional point on the vapor pressure curve. The equation w w tested n i t h seven gases GO2,HzO, COHS,N2, C8HB,€1253, and C31T8,and found to give a maximum error of 1.0% up to one and one-half times the critical density. In specific studies Canjar and others (10B)have correlated the eight constants in the Benedict-Rubin-Webb cquation of state for straight-chain hydrocarbons. Critical temperature and namber of carbon atoms are the parameters in the corrclation. Wolemann and Hasselmann (f?OB) have developed the following equation for acetylene:
- aP - bP2 a = 0.489 - 1.08 X b = 6.99 X 10-3 - 2.1 X
PV
=
RT
(4) (5) 1OV6T
(6)
P = atmospheres T=="K. For nitrogen I'aoluzi ( S 7 B ) has used Rn expression of the form: a
RT
(7)
Over the range 0" to 400" C. and 50 t o 400 atm. the results are apparently more accurate than those predicted from the HeattieBridgman equation of state. Vapor Pressure. The vapor pressure of zirconium fluoride x a s determined from 616" to 881" C. ( 4 3 B ) and correlated by an equation of the form log P = A 4BIT. The heat of sublimation a t 900" C. was found to be 56,630 cal. per gram mole. The Calingaert-Davis equation was used to fit measured data ( 5 4 6 ) from 80" to 150" C. for p-nitroethylbenzene and o-nitroethyl-
J. M. SMITH received his B.S. degree from California Institute of Technology in 1937 and Sc.D. from MIT in 1943. Smith is professor of chemical engineering and assistant director, Engineering Experiment Station, Purdue University. During 1953-54 he was a Fulbright research scholar a t Technische Hogeschool, Delft, Netherlands. N e is author of a thermodynamics text and a member of the ACS, ALChE, ASEE, and Sigma Xi. March 1956
benzene. Other vapor pressure measurements of possible interest to chemical engineers were reported for ferrous bromide (.SOB) and trimethythydrazine (bB). A generalized vapor pressure correlation on a reduced basis was included in Lydersen, Greenkorn and IIougen's work (ZQB). The result is as follon-s:
where
P R =~ reduced vapor pressure
T R =~ reduced boiling point The parameter A was related to the compressibility factor a t the critical point 2, in the following way:
3 15 3.14 3 . 1 0 3.02 2 90 2.76 2.50 1 . 8 0 0.23 0 24 0.25 0.26 0 27 0.28 0 . 2 9 0.30
A
Z,
P-V-TData. Experimental volume data were determined for neon (366) from 10 to 80 atm. and from 0' to 700' C. The results were used to evaluate virial coefficients and intermolecular force constants. The measurements of Singh and Shemilt on n-butyl alcohol included the liquid and vapor regions and indicated the following values a t the critical point: P,
= 48.6 atm.
tc = 286.9' C. pc =
0.27 grams per cc.
Investigations of mixtures included a study by Bloomer, Gami, and Parent ( 7 B ) of eight mixtures of methane and ethane over a temperature range of -210' to 90" F. and from 50 to 998 pounds per square inch absolute. The volumes are believed to be accurate to 0.3%. compressibility factors of ozone were computed from the critical constants and combined with experimental data for oxygen t o arrive a t compressibility factors for the oxygen-ozone binary system (6B). Petty and Smith (dQB) measurcd volumes in the polar-nonpolar system n-butanemethanol from 120" t o 280" F. and up t o 700 pounds per square inch ahsolute. The results indicated deviations of as much as 10% from the conventional compressibility factor chart in terms of reduced pressure and temperature. Lambert and others ( % B ) determined second virial coefficients from volumetric data on t,he following mixtures: Cyclohexane-diethylamine C yclo hexane-acetone Cyclohexane-acetonitrile The partial volumes of benzene, methane, ethane, and propane in aqueous solutions were determined ( S d R ) from 10' to 40" C. The partial volumcs were le65 than those for the same hydrocarbons in nonpolar solvents.
C. 0. BENNETT is an associate professor of chemical engineering at Purdue University, where h e has been a member of the staff since 1949. During the 1952-53 academic year he was a visiting lecturer in chemical engineering at the University of Nancy, France. His principal research interest is in high pressure phenomena. H e received the B.S.degree from Worcester Polytechnic Institute and the D.Eng. degree from Yale University.
INDUSTRIAL AND ENGINEERING CHEMISTRY
677
FUNDAMENTALS REVIEW
Addition of a third parameter has improved the general compressibility chart.
..
Critical Properties. The critical constants for saturated and unsaturated aliphatic hydrocarbons have been correlated by Thodos ( 5 0 B ) using a group contribution method; that is, a contribution to the van der Waals constants is assigned for each structural group of the molecule. These constants are related to the critical properties. A group contribution approach for all types of substances has been suggested by Lydersen ( d 8 B ) . The equation for T , is:
xb
= 0.567
+-
T C
ZAT
-
AT)'
(9)
Tb = normal boiling point T , = critical temperat)ure
AT = contribut,ion of the structural group t,o the ratio Tb/T,
Similar expressions are given for the critical pressure and volume. Heat Capacity. The specific heat of ethyl alcohol has been measured (44R)calorimetrically over a rr-idc range of condit,ions, covering 1 to 118 at,m. and -60" to 235' C. Other studies on pure components were reported for lead sulfide, lead selenide, and lead telluride ( S 8 B )and silver iodide (26H). I n the relatively unexplored area of mixture heat capacities, data were published for liquid phenol-water mixtures from 60" to 70" C. (22%) and for liquid mixtures of benzene--ethylene dichloride, benzene-. carbon tetrachloride, acetone-chloroform, and acetone-carbon disulfide (47'B). The latter measurements were made from 15' to 75' C. all a t 1 atm. pressure. Heat Effects. Heat of mixing data wcre reported for seven binary systems involving acetone, nitriles, and amines by Thacker and Itowlinson (49B). Similar information was determined by Canning and Cheesrnan ( I I R )for six pairs of t,he four components benzene, toluene, benzyl chloride, and benzyl bromide. All these data ivere obt,ained at 25" C. By considering the association of methanol, equations were developed by I
