Specific Heat Ratios for Hvdrocarbons W. C. EDMISTER, Standard Oil Company (Indiana), Whiting, Ind. The second derivative was determined graphically from the
A chart is presented for estimating CJC,
a, correlation, Equation 3 was integrated, and values ' of
(7) ratios for methane, ethylene, ethane, propylene, propane, isobutylene, isobutane, 2-butene, n-butane, isopentane, n-pentane, benzene, diisopropyl, n-hexane, nheptane, diisobutyl, and n-octane at reduced pressures up to 1.2 and at reduced temperatures up to 2.5.
AC,/K2 were tabulated ( I ) . From these results the effect of pressure on the isobaric specific heat can be computed. The effect of temperature on the specific heat can be calculated by the correlation of atmospheric specific-heat data (1). Upon the introduction of ar and reduced units, Equation 2 becomes:
T
HE ratio of isobaric to isometric specific heats, Cp/Cv=
y, is a n essential thermodynamic property in calculations involving the adiabatic compression or expansion of a gas. It may be determined experimentally or computed by thermodynamic relations from P-V-T and atmospheric specific-heat data. There are few y data, either experimental or calculated, for hydrocarbons, however. Some experimental y data are available (3) a t atmospheric pressure for hydrocarbons of one to six carbon atoms. Values a t various pressures have been computed and plotted only for methane (2).
The derivatives of CY? were determined graphically from the arcorrelation and were tabulated (1).
Calculation and Correlation of C,/C, The computation of C,/G ratios from these equations and reduced thermodynamic functions were made for various reduced temperatures and pressures for seventeen hydrocarbons, and the resulting C,/C, ratios were plotted against P, for lines for constant T,. One of these plots (for propane) is shown in Figure 1. Comparison of the plots showed that they were very similar and that all of them could be made to coincide by either expanding or condensing their C,/C, scales. I n other words, Figure 1 for propane will hold equally well for all the other hydrocarbons if different numerical values are given the ordinate scale. This is done by the following equation:
Basic Equations The two fundamental thermodynamic equations used in computing C,/C, ratios from P-V-T and atmospheric specific heat data are: =
--T
Y =
where 7s
1
+
C(Y8
- 1)
value of C,/C, for propane C = constant for each hydrocarbon (Table 1) y = Cp/Cvfor the hydrocarbon in question =
The integration constant for Equation 1 must be found from experimental isobaric specific heat data. Although data a t any pressure could be used, data only a t atmospheric pressure are available. The volume derivatives for the above equations can be determined graphically or analytically from P-VT data by means of graphic or algebraic equations of state. I n a previous paper ( I ) a generalized reduced correlation of P-V-T data for hydrocarbons was developed by using the volume residual quantity, a, which is defined as the difference in the ideal and the actual gas volumes. The resulting correlation gave the reduced volume residual quantity, a?, as a function of reduced temperature T , and pressure P,. When expressed in terms of a, and reduced units and integrated between the limits of P, and P,= 0 a t constant values of T,, Equation 1 becomes:
where AC,
6
Kz =
increase in isobaric specific heat from 0 pressure to any pressure P, P , ac/Tcra constant for each hydrocarbon
FIQURE 1. PLOTFOR PROPANE 373
(5)
INDUSTRIAL AND ENGINEERING CHEMISTRY
374
FIGURE
2.
GRAPHICAL METHOD FOR
By means of Figure 1, Table I, and Equation 5 the C,/C, ratio can be estimated for all seventeen of the hydrocarbons listed in Table I for the range of temperature and pressure covered by Figure 1. Figure 2 combines Figure 1, Table I, and Equation 5 to present a rapid graphical method for estimating y . I n constructing Figure 2, the pressure and temperature ranges were extrapolated. The solution of an example is shown by heavy dashed lines and arrows; we find y = 1.525 for propylene a t P, = 0.555 and T, = 0.95. TABLEI. CONSTANTS FOR SEVENTEEN HYDROCARBONS Value of Constant Hydrofor Equation 5 carbon Methane 3.5 Ethylene 2.1 Ethane 1.58 Propylene 1.17 Propane 1.00 Isobutylene 0.810
Value of Constant Hydrofor carbon Equation 5 Isobutane 0.778 2-Butene 0.737 n-Butane 0.705 Isopentane 0.590 n-Pentane 0.541 Benzene 0.525
Value of Constant Hydrofor carbon Equation 5 Diisopropyl 0.442 n-Hexane 0.442 n-Heutane 0.364 Diisobutyl 0.300 n-Octane 0,300
Accuracy of Correlation Figure 2 gives values of y that check the values computed from the original P-V-T correlation with a maximum deviation of *4 per cent. Most of the points are checked within 1 per cent by the correlation.
VOL. 32, NO. 3
ESTIYATING y
As a test of the above correlation, values of y from it were compared with the atmospheric pressure experimental data from the International Critical Tables (3). The maximum deviation was 4 per cent. A comparison a t higher pressure would be more severe and of more interest, but unfortunately there are no high-pressure experimental y data. Application of Results The Cp/Cvratio is primarily of use in calculations of isentropic expansion and compression of gases. The following equation for the theoretical horsepower required for single stage adiabatic compression of gas is based upon the assumption of perfect gas behavior:
I n such processes neither pressure nor temperature remains constant, but each necessarily varies. The conventional use of Equation 6 is with a constant specific-heat ratio throughout the process. For want of better data, the atmospheric pressure y or even the y for air is frequently used for hydrocarbons. Such a procedure will cause appreciable errors in many cases. Figure 2 shows that y varies widely with temperature, pressure, and molecular weight. Although a rigorous solution of Equation 6 would require integration with y as a variable, sufficient accuracy for engineering purposes is ob-
MARCH, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
tained when y is considered constant at an average of the values at the inlet and outlet conditions. The use of Equation 6 with y values from Figure 2 is a step in the right direction but does not correct for the fact that Equation 6 is based on perfect gas law behavior. However, the effect of deviation from ideal gas law behavior on Equation 6 is not so important as the effect on y; therefore the use of Figure 2 should greatly improve the accuracy of such computations. I n engineering work the compression and expansion of mixtures is frequently encountered. y for mixtures may be determined by computing the molal average of y values of the individual components, the y for each component being determined for the temperature and total pressure involved.
375
-
Acknowledgment The author is indebted to the following Evening Division graduate students in chemical engineering a t Armour Institute of Technology for assistance in the thermodynamic computations: E. C. Berger, D. G. Debo, C. H. Deuter, W. E’. Findling, C. Giuliani, W. A. Hoyer, E. B. Lund, A. H. Maack, U. G. Naef, E. L. Niederhofer, N. C. Penfold, A. G. Petkus, J. C. Reidel, J. D. Schulz, and G. Thodos.
Literature Cited
~
~2
&$ ~ ~~ :~(lg3’). , ~ ~ ~~ ~; ~ , 3
(3) International Critical Tables, Vol. V, p. 80, New York, McGrswHill Book Co., 1929.
Infrared Absorption Spectra of Drying Oils
D. L. GAMBLE AND C. E. BARNETT The New Jersey Zinc Company, Palmerton, Penna.
The application of the methods of infrared absorption spectra in the study of the drying oils is described. The discussion includes the following items : the spectra of the drying oils and the effect of pigmentation on the spectra, the absorption spectra of the pure esters of the drying oil fatty acids, the effect of conjugation on the absorption, changes in the infrared absorption spectra caused by exposure of the esters to ultraviolet light and oxygen, and the effect of polymerization on the spectra.
T
HE economic importance of the physical and chemical
changes which take place during the formation and decomposition of films of the drying oils is such that these reactions have been the subject of constant investigation for a number of years. The purpose of this paper is to present results indicative of the possibilities of the method of infrared absorption spectra as applied to this general problem. The peculiar efficacy of the infrared absorption technique lies in the fact that it is a physical method with no chemical effect on the paint film; therefore, it permits repeated examination of the specimen in which progressive changes are taking place. Since many pigments are transparent in the infrared, the measurements are unaffected by the presence of pigments, and thus the method offers the possibility of studying the effects of pigments on the changes occurring in the vehicle during drying and aging. Excellent discussions of the theory and interpretation of infrared absorption spectra as applied to organic compounds will be found in the literature (1, 5 ) .
Apparatus and Procedure The apparatus described in the previous paper (2) was modified somewhat for this work: A Nichrome glower was used as the source of radiation although it is weak at wave lengths beyond 10.0 microns; flters
(7) were used to remove contaminating radiation. Since glass is opaque in the infrared beyond 6.0 microns, samples are examined in rock salt cells, as films on rock salt plates, or often without any backing. Thick cells may be made with rings of known thickness as separators, while for thin cells thin tinfoil is a suitable material. The cell is held together with clips or with any adhesive that is not attacked by the sample. Pigmented films may contain from 20 to 40 per cent by weight of pigment and are usually prepared for examination by brushing out the paint on a plate of polished rock salt. The absorption spectra of such a film may be measured wet or dry or after any desired period of exposure; the same film is used throughout, and the absorption spectra are determined a t various stages in its life. Films may be prepared on amalgamated panels, and sections may be removed as desired and mounted directly without any backing. The thickness of the films should be carefully controlled. The best way to do this is by measurement of the transmission through the film a t some wave length where there is a minimum of absorption.
As an indication of the sensitivity of the spectrometer, Figure 1 (left) shows the absorption spectrum of linseed oil compared with the published curve of Stair and Coblenta (8) and with the results obtained with a grating spectrometer which was set up t o study the region between 5.0 and 8.0 microns more closely. The agreement between the two prism spectrometers is good, or at least the difference between the two is insignificant in view of the difference between either one and the grating spectrometer.
Absorption Spectra of China Wood and Linseed Oils Figure 1 (right) shows the absorption spectra of linseed oil, China wood oil, and oiticica oil from 2 to 12 microns. Absorption bands are found in the first a t 3.4, 5.8, 6.9, and 8.4, and 11.5 microns and in addition a t 10.0 microns in the China wood and oiticica oils. The bands a t 3.4 and 6.9 microns are due to the G - H vibration and that a t 5 3 to the C 4 ; the band a t 8.4 microns has been variously ascribed to C = O (9), C-C (S), and (OH) (4). Lecompte (5) lists this as a characteristic absorption of esters which varies somewhat with the composition of the ester: “Our personal opinion is that these changes are attributable to the acid radical which serves to form the ester, rather than to the alcohol radical.” For the purpose of this paper it is enough to ascribe it to the presence
