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JAMES R. WEST
tatively for sodium palmitate, sodium oleate, and sodium myristate. The results are found to be in good agreement with observation, not only in reproducing the experimental hydrolysis curves, but in obtaining their temperature coefficients. REFERENCES (1) ADW, N. K.:The Phydcs ond Chemistry of Surfactx, Table IV, p. 64. Oxford University Press, London (1961). (2) COOK,M. A., AND NIXON,J. C.: J. Phys. t Colloid Chem. 64,445 (1950). (3) LONQ,F. H., NWTTINQ,G. C . , AND HARKINS, W. D.: J. Am. Chem. Soo. 69,2179 (1939). LONQ,F. H., AND NUTTING,G. C: J. Am. Chem. Soc. 63, &4 (1941). (4) LOTFERMOSER, A.: Trans. Faraday Soc. 81,200 (1936). LOTFERMOSER, A., AND GIESE, E.: Eolloid-2. 43, 276 (1935). (6) POWNEY, J., AND JORDAN, D. C.: Trans. Faraday 800. 84, 363 (1938). (6) STAINSBY, G., AND ALEXANDER, A. E.: Trans. Faraday Soo. 46, 585 (1949).
T H E THERMAL CONDUCTIVITY OF SULFUR VAPOR JAMES R. WEST'
Mellon Institute, Pitkburgh 13, Pennsylvania Received March 16, 1960 INTRODUCTION
Early workers confined themselves to measuring the thermal conductivity of rhombic or of plastic sulfur (2, 4, 8). The results of the sole comprehensive investigation that included rhombic, monoclinic, plastic, and liquid sulfur are shown graphically in figure 1 (5). Although nothing has been published about the thermal conductivity of sulfur vapor, it is possible to make an estimate of this property for the vapor, as described below. CALCULATIONS AND RESULTS
First, it is w u m e d that sulfur vapor consists of octatomic, hexatomic, and diatomic species in the temperature range of 450"to 1oOO"C. (6,7, 10).Secondly, it is sssumed that, for any one species, the difference between the heat capacity at constant pressure and that at constant volume is equal to the gas constant (1.987 cal. per g.-mole per degree Kelvin). From K. K. Kelley's work the following heat capacity equations at constant pressure were derived for the three molecular species (e)? c, (SS)= 25 3.5 x lOJT C, (Ss)= 19.25 2.64 X lOdT C , (S2)= 7.75 0.888 X 1W'T
+ + +
Senior Fellow, Mellon Institute, Pittsburgh, Pennsylvania, on the Multiple Fellowship sustained by the Texas Gulf Sulphur Company, New York, New York. * Meaning of the symbols used: C , (SI) = heat capacity at constant pressure of octatomic sulfur vapor, in calories per gram-mole per degree Kelvin,
THERMAL CONDUCTIVITY OF SULFUR VAPOR
403
As shown in table 1, the ratio of the heat capacity at conetant preasure to that at constant volume waa found to remain relatively constant for each species from 25' to 1OOO"C.
50
100 150 200 TEMPERATURE (0
250
FIG.1 Thermal conductivity of sulfur
The Prandtl numbers shown in table 2 were next estimated for each type from the formula by W. H. McAdams (9). G. A. D a h and J. R. West have outlined a method of computing the viscosity of the individual species (1). From these C, (S6) = heat capacity a t constant pressure of hexatomic sulfur vapor, in calories
per gram-mole per degree Kelvin,
C,
(S2)
= heat capacity a t constant pressure of diatomic sulfur vapor, in calories
per gram-mole per degree Kelvin,
k (SS) = thermal conductivity of octatomic sulfur vapor, in C . G . S . units, k (Sa) = thermal conductivity of hexatomic sulfur vapor, in C . G . S . units, k (Sz)= thermal conductivity of diatomic sulfur vapor, in C.G.S. units, = thermal conductivity of equilibrium sulfur vapor a t 1 atm., in unita, P r (Sr) = Prandtl number of octatomic sulfur vapor, dimensionless, P r ( 8 6 ) = Prandtl number of hexatomic sulfur vapor, dimensionless, Fr (SI)= Prandtl number of diatomic sulfur vapor, dimensionless, p (S,) = viscosity of octatomic sulfur vapor, in CAS. units, p (SS) = viscosity of hexatomic sulfur vapor, in C.Q.S. units, and 1.1 (Sz) = viscoeity of diatomic sulfur vapor, in C.Q.S. units.
k (average)
C.Q.S.
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JAMES R. WEST
TABLE 1 Ratio of heat capacities
T. 25 500 loo0 Average
I
1.082 1.077 1.072 1.077
1.110 1.103 1.096 1.103
1.330 1.308 1.289 1.309
TABLE 2 Prandtl numbers PM"%
YOLLWIAP SPECIES OB SULFUR
Octatomic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hexatomic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diatomic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I . . .
I
NUYBDP
0.92 0.89 0.77
FIG.2. Thermal conductivity of sulfur vapor
data values of the thermal conductivity of each species were calculated by meane of the following formulae:
THERMAL CONDUCTIVITY OF SULFUR VAPOR
405
At 1 atm. total pressure the values of the thermal conductivity illustrated in figure 2 were obtained from the following relationship:
k (average) = Y (88) k (Sa)
+ Y (Sa) k (Sd + y (SP)k (SO)
In the equation immediately above, yn defmes the respective mole fractions obtained from an article by J. R. West (11). DISCUWION
No experimental measurements have been made to confirm these computations. The exact molecular constitution of sulfur vapor has never been proven conclusively; hence these calculations are subject to doubt (3). Quite probably the method used for obtaining the average values also introduced some error. The results, however, are considered suitable for estimational purposes in the absence of any other information, if used with caution. SUMMARY
The thermal conductivity of sulfur vapor at 1 atm. has been estimated as a function of temperature. Thanks are given to the Texas Gulf Sulphur Company and to W. W. Duecker of that organization for support. The writer is grateful to L. H. Cretcher and W. A. Hamor of the Mellon Institute for their assistance in the preparation of this article. REFERENCES
(1)DALIN,G. A.,AND WEST,J. R.: J. Phys. & Colloid Chem. 64, 1215 (1950). A.: Ann. Physik 34, 185-222 (1911). (2) EUCICEN, (3) GLASSTONE, S.: Teztbook of Physical Chemistry, 2nd edition, p. 320. D. Van Nostrand Company, Inc., New York (1946). (4) HECHT,H.:Ann. Physik 14, 1008-30 (1904). (5) KAYE,G. w. C., AND HIGGINS,W. F.:Proc. Roy SOC.(London) A l a M633-48 , (1929). (6)KELLEY,K. K.: U. S. Bur. Mines Bull. No. 406 (1937). (7)KLEMM,W., A N D KILIAN,H.: 2. physik. Chem. B49, 279-83 (1041). (8)LEES, C. H . : Phil. Trans. A l a , 481-509 (1892). W. H.: Heat Transmission, 2nd edition, p. 21. McGraw-Hill Book Company, (9)MCADAMS, Inc., New York (1942). (10)PREUNEB, G., AND SCHUPP,W.: 2. physik. Chem. 66, 129-56 (1910). (11)WEST,J. R.:Ind. Eng. Chem. 42,713-18 (1950).
