Vol. 23, No. 11
I N D U S T R I A L A N D ENGINEERING-CHEMISTRY
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trolled by means of the needle valve so as to maintain a zero temperature difference between the container and the jacket as indicated by a difference thermocouple. The values determined are 33.9 calories per gram (4100 calories per mole) at 23" C., and 32.8 calories per gram (3960 calories per mole) at 28" C., with an estimated accuracy of 2 or 3 per cent. Ratio of Specific Heats of the Vapor
The specific-heat ratio C,/C. = y, of dichlorodifluoromethane vapor was measured a t 25" C., and atmospheric pressure by the Kundt method. The velocity of sound in the vapor relative to that in air was measured in a Pyrex tube, 4.3 cm. in diameter and 135 cm. long, a t a frequency of approximately 2700 cycles per second. The sound waves were produced by stroking a clamped brass rod with a cloth moistened with methanol and were transmitted t o the air or vapor by means of a thin brass disk mounted on the end of the rod, just inside the end of the tube. Resonance was obtained by moving a similar disk in the other end of the tube; the positions of the nodes were indicated by cork dust. Displacement of the heavy vapor by air was prevented by tying thin sheet rubber over the ends of the horizontal tube and by maintaining a slow stream of vapor through the tube with upward exit. The measured velocity ratio relative to air was 1:2.298. Several other measurements of somewhat less accuracy gave values for the ratio within less than 0.5 per cent of this figure.
I n particular, reduction of the tube diameter from 4.3 to 2.0 cm. did not affect the result within the limit of error of individual determinations; therefore no tube correction was applied. The velocity of sound in air a t 25" C. was calculated from the equation in the International Critical Tables ( 3 ) , with a slight correction for 3 mm. partial pressure of water vapor as 34,640 cm. per second. The velocity in the dichlorodifluoromethane was therefore 15,073 cm. per second. The value of y was then determined as 1.139 * 0.005 by substituting the proper values in the following form of the Laplace equation (2):
W M V ($)T
= velocity of sound = 15,073 cm. per sec. = molecular weight = 120.9 = volume per mole = 25,000 cc. =
-38.42 dynes per sq. cm. per cc. per mole
The values for V and
(g)T
a t 25' C. and 0.96 atm. were
obtained from the equation of state ( 1 ) .
Literature Cited (1) Buffington and Gilkey, IND. ENG. CHEM.,23, 254 (1931). (2) Cornish and Eastman, J . Am. Chem. SOC.,50, 639 (1928). (3) International Critical Tables, VI, 462 (1926).
Thermodynamic Properties of Dichlorodifluoromethane, a New Refrigerant V-Correlation, Checks, and Derived Quantities' Ralph M. Buffington and W. K. Gilkey FRICIDAIRE CORPORATION, DAYTON,OHIO
This is the concluding member of a series of papers contains, i m p l i c i t l y or exHIS p a p e r completes which provide the basis for engineering tables of the plicitly, consistent values of the report of a program 0f resear ch thermodynamic properties of dichlorodifl,uoromethane. a l l t h e t berm 0 d y n a m i c Application of thermodynamics to an equation of state quantities which are of inwhich was undertaken for the for the vapor, to a vapor pressure equation, to a graph terest. The network is then purpose of providing the basis of the density of the liquid, and to an equation for the checked a t various points by for thermodynamic t a b l e s specific heat of the vapor at 1 atmosphere, results in a means of additional secondneeded in t h e d e s i g n and operation of dichlorodifluoronetwork, which contains consistent values of all the ary data, and perhaps by required properties, for the region between the isomeans of empirical rules, thus methane refrigerating equipmerit. The e x p e r i m e n t a l metrics which correspond t o saturation at -40' and m a i n t a i n i n g a continuous 50" C. The network is checked by means of secondary check on its accuracy. data, and e q u a t i o n s a n d data. Derived results are given, in the form of equagraphs r e p r e s e n t i n g them, Thermodynamic Network tions or graphs, for the following: the latent heat of have been given in e a r l i e r vaporization L; C, and C, of the vapor; C, of the The network has been built papers of the series, and the liquid; and the entropy s and heat content H of the up from the following: an tables have been published elsewhere (4). It remains liquid, saturated vapor, and superheated vapor. equation of state for the superheated vapor ( 3 ) , a vaporfor this paper to present the correlation of the data, the thermodynamic checks, and the pressure equation (5),a graph of the density of the liquid ( I ) , and an equation for the specific heat of the vapor at atmoscalculation of derived quantities. Because of the thermodynamic relations existing between pheric pressure ( 2 ) . The notation used is as follows: the various properties, there is room for only a few independent equations expressing experimental results. The procedure adopted has therefore been to determine experiC, = specific heat a t constant pressure in cal. per gram mole c. m e n t a b a few fundamental quantities Over a range of presheat at constant volume in tal. per gram mole c, = sure and temperature and express the results empirically, c. V = volume of vapor in liters per gram mole and then to combine them with exact thermodynamic formulas, thus constructing a thermodynamic network which P = pressure in atmospheres
T
T = absolute Centigrade temperature ( " C.
1 Received
August 13, 1931.
v
+ 273.1)
= volume of liquid in liters per gram mole
INDUSTRIAL AND ENGINEERING CHEMISTRY
November, 1931
L
= latent heat in cal. per gram mole
L
H = heat content in cal. per gram mole S = entropy in cal. per gram mole " C.
= 560.17
C
1293 T
- 12.94 ( T , - T)
(3)
where T, = 384.6", the average deviation being less than T, = critical temperature on absolute scale ( = 384.6") 0.2 per cent. The graph of this equation is shown in All purely thermodynamic equations are written on the Figure 1. SPECIFICHEATSOF VAPoR-The thermodynamic relaassumption of consistent units; the necessary conversion factors are introduced along with the empirical data. tions between the specific heat of a substance and its equaVOLUMES OF SATU- tion of state may be summarized as follows: R A T E D VAPORThe first step in the 4 5444 Q formation of the net%044 work is the calculation of the volumes 8I 3404 h of saturated vapor $2 000 by the simultaneous solution of the va- These relations suffice for the calculation of C, and C, a t loo4 por-pressure equa- all temperatures and pressures from the equation of state, tion and the equa- and a value of either C, or C, a t each temperature and some -20 0 a4 M mo iTEMP€RRRTL/RE- DE6REES C€NTlGR#OE tion of state. The particular pressure. Figure 1-Graph of E q u a t i o n 3 r e s u l t s have been It is simplest t o start from a consideration of the isometrics Circles represent experimentally determined latent heats of vaporization. given in an earlier (the pressure-temperature relations a t constant volume). paper ( 1 ) . The cal- Experimentally and also according to the equation of state, culation was carried out a t 10" C. intervals between -40" and the isometrics of superheated dichlorodifluoromethane vapor 50" C., using Homer's method for the solution of the cubic are straight lines in the region covered by the measurements. equations involved. This procedure is practically equiva- This is the usual approximation for low and moderate preslent to a direct experimental determination, as the isometrics sures, and greatly simplifies the mathematics of the probon which the equation of state was based were carried close lem. For (6p/6T)v = constant, and ( 6 ? p / 6 T 2 ) y = 0; hence, to the saturation line; and it has the advantage of automati- by Equation 4 C, is independent of volume and a function cally correlating the saturated volumes with the vapor- of temperature only. On the other hand, (61'/6T), # pressure equations and the equation of state. Intermediate constant, and (62V/6T2)p# 0; hence, by Equation 5 C, values were obtained by an interpolation method, in which is a function of both pressure and temperature. For most the deviations of saturated volumes from the perfect gas law value, R T / p , were plotted against V . Less accurate I I values above 50" C. were obtained by other methods (1); I these are not used in the network. LATENTHEAT OF VAPORIZATION-The latent heats, the volumes of saturated vapor, and the slopes of the vaporpressure equation are related by the Clausius-Clapeyron equation, any two of these quantities sufficing to fix the third. It was elected to determine the latent heats in this way, preliminary calculations having shown that the resulting values of the Hildebrand and Trouton constants would be reasonable. The exact Clausius-Clapeyron equation was used, in the form
*
PO
40
~1
I ill1 properties are taken a t saturation. Equation 1 was solved for L a t 10" C. intervals, between -40" and 50" C., a t the temperatures for which the volumes of the saturated vapors were known; p was obtained from the vapor-pressure equation, loglo P = 31.6315
1516 5 - --iG - 10.859loglo T
+ 0.007175 T; (2)
d loge
P
40
-
BO
/ZO
TEMPERATURE DEGREES CENT/GRAD€ Figure 2-C, of Vapor Calculated from equation of state and Cp a t 1 atmosphere.
computational purposes, therefore, C, is more useful than C,. The available specific heat data ( 2 ) are, for a constant pressure of 1 atmosphere: Cp (1 stm.) = 9.39
+ 0.0279 T
C. was calculated by the following process: was rewritten in the equivalent form,
(7)
Equation 6
(+) was obtained from the derivative of the vapor-pressure equation, and v from a graph of the density of the liquid. In order to obtain intermediate values of L and also t o obtain approximate values a t higher temperatures, the ClausiusClapeyron values of L and the critical temperature were used t o determine the constants of an empirical equation (6) which is known to represent accurately other latent-heat data. A practically perfect fit was obtained with the following equation for the molal latent heat of vaporization:
as ( 6 p / 6 V ) is ~ much more readily evaluated than (6V/6T),. The equation of state (3) was then written in form for differentiation:
whence
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
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Vol. 23, No. 11
Checks The agreement between the observed values of the latent heat and those calculated from Equation 3 is shown in Table I.
and
between Observed a n d Calculated Values of Latent Heat ESTD. L EXPTL. OBSD. CALC. A DEVIATION ERROR Cal./mole Cal./mole lo % 4880 4832 1.0 2 4100 4125 0.6 2-3 3970 4038 68 1.7 2-3
Table I-Agreement
Substituting in Equation 8, introducing the values of the constants ( R = 0.08207, AO = 23.7, a = 0.305, Bo = 0.59, and b = 0.622), and simplifying,
c, - C" =
2.881
Substituting simultaneous values of V and T at 1 atmosphere and combining the values of C, - C, so obtained with C, from Equation 7, a series of values for C, a t 1 atmosphere were obtained, which were then accurately fitted by means of the linear equation, C, = 6.92
+ 0.02894 T
(13)
As noted above, C, is required to be independent of volume; hence Equation 13 is applicable a t all pressures and temperatures within the range of validity of Equations 7 and 9. Values of C, - C, were than calculated for a series of temperatures and pressures, and combined with values of C, from Equation 13 to give representative values of c, over the entire field. These are plotted in Figure 2. The general form of the C, curves is quite similar to that for other vapors. ENTROPY AND HEAT COXTENT-FOr purposes of calculation it is convenient to consider the changes of state as combinations of changes along an isometric, along an isotherm, and across the saturation line. The change in entropy along an isometric of the vapor is found by substituting C, from Equation 13 into the thermodynamic expression, dS. = C,dT/T, and integrating:
+ 0.02894(T - To) dH, = C d T + Vdp
AS, = 15.925 loglo Similarly,
T
(14) I
and
AH, = 6.916(T - To)
+ 0.01447(T 2 - To2)+ 24.204 V ( $(15) - Po)
For the change along an isotherm of the vapor, dSb = (Gp/ST)vdV
and
mb=
-24.204
[(0.0484T - 47.4)($ -1&) 1 - (0.0302T - 10.85) (p - m )]
(17)
For the process of vaporization,
It will be observed that repetitive calculations are greatly simplified by the duplication of terms.
t
C. - 23 30 O
28
2;: -
The probable error in the calculated values of L is about 2 per cent. A check on the specific heats of the vapor a t low pressures is afforded by the determination of y = C,/C, by a velocity of sound method (d). The measured value was 1.139 * 0.005 a t 25" C. and 1 atmosphere; from Equations 7 and 13, y = 1.138. The network contains a complete set of values for the heat content of the liquid along the saturation line, and hence of its specific heat, for the range from -40" to 50" C. The calculation is an indirect one, involving a considerable part of the fundamental data. The values thus obtained can be compared with the experimental specific heats of the liquid, thus obtaining the best over-all check on the network now available. (Entropy instead of heat content could be used for this check with identical results.) The methods outlined in the preceding section were applied to the calculation of the heat content of the liquid along the saturation line, starting from liquid a t -40" C., vaporizingit a t that temperature, heating the vapor a t constant volume up to the required temperature, and then compressing it isothermally and condensing it. Values of the heat content of the liquid were thus found for successive points. The change in heat content per degree along Figure 3-Straight Line Repthe saturation line is called C,, resenting Values of Cp of Liquid disregarding the very small according to Network A and B are experimental points. change of heat content with pressure. The values of C, ihus obtained lie well on a straight line (Figure 3), but do not agree well with the experimental values, the difference being about 8 per cent. However, considered as a check on the network, the agreement is quite satisfactory, the probable error in the direct measurement of C, (4 per cent) and in Equation 3 for the latent heat (2 per cent) being more than sufficient to account for the deviations. There is no reason to believe that the thermal properties of the vapor are in error to any great extent. The indicated accuracy of the calculated C, of the liquid is ample for applications involving vaporization or condensation, as the specific-heat term is small compared with the latent heat. For instance, perhaps the most important calculation involving C, of the liquid is that of net refrigerating effect. An 8 per cent error in C, would cause a 3 per cent error in the typical case, with a good possibility that this error is largely compensated by a corresponding error in L. Literature Cited Bichowsky and Gilkey, IND. ENG.CHBY.,23, 366 (1931). Bu5ngton and Fleischer, Ibid., 23, 1290 (1931). Bu5ngton and Gilkey, I b i d . , 23, 254 (1931). Buffington and Gilkey, Am. SOC.Refrigerating Eng., Circ. 12 (1931). Gilkey, Gerard, and Bixler, IND.ENG.CHBM.,23, 364 (1931). Osborne and Van Dusen, Bur. Standards, BuU. 14, 439 (1917).
