INDUSTRIAL A N D ENGINEERING CHEMISTRY
April, 1944
reference line downward; this was not done in the figure because of confusion with the other lines.) To use the nomogram, the temperature and X scales are connected with a straight line. The point at which this line crosses the reference line is then connected with the C scale; and the extension of this second construction line to the left gives, on the pressure scale, the value of the partial pressure of carbon dioxide exerted by such solutions. The combination of scales
311
may be used to obtain the value for any one of the other four variables provided three are known, LITERATURE CITED
(1) Harte, C. R., Jr., Baker, E. M., and Purcell, H. H., IND. ENQ. (2) Othmer, CREM., D. 25,F., 528 I ~(1933). ~32,~841 . ,(1940). (3) Ibid., 34, 1072 (1942). (4) Othmer, D.F.,and White, R. E., Ibid., 34, 952 (1942).
Specific Heat of Zirconium Dioxide at Low Temperatures ENTROPY AT 298.16O K.
K. K. KELLEY Pacific Experiment Station, U. S. Bureau of Mines, Berkeley, Calif. The specific heat of crystalline zirconium dioxide was measured throughout the temperature range 52' to 298' K., and the entropy was computed as S O 2 9 8 . 1 8 = 12.03 * 0.08. The entropy and free energy of formation from the elements are, respectively, A S o 2 9 a . 1 6 = -46.5 and A F O 2 s s . 1 6 = -244,200.
T
.
HE determination and correlation of fundamental thermal data of substances of metallurgical interest have been activities of the Bureau of Mines for several years. Some time ago, a t the request of the industry, an investigation of the low-temperature specific heat of zirconium dioxide was undertaken, The zirconium dioxide was furnished by J. C. Southard of the Titanium Alloys Manufacturing Company. It was a crystalline product that had been crushed to about 40-mesh size after electrical fusion. Analyses furnished by the company indicated a purity of 99.14%. The principal impurities were 0.30% SiOz, 0.20% TiOz, and 0.07% CaO. The remaining 0.29% was divided among several other oxides; none was present in an amount greater than 0.05 yo,according to the spectrographic analysis. The specific-heat measurements were made by methods and apparatus described previously ($2). The defined calorie is used (1 calorie = 4.1833 international joules), and the molecular weight of zirconium dioxide is taken as 123.22 grams in accordance with the 1941 International Atomic Weights, The measured results, in calories per mole per degree, are listed in Table I and shown in Figure 1. They have been corrected for the effects of the principal impurities, assuming that the specific heats are additive. The correction varied from 0.54% in the lowest to 0.05% in the highest recorded specific-heat value. The specific heat a t room temperature is about 0.5 calorie per mole higher than given by the equation derived previously (3) by the author on the basis of less reliable data at higher temperatures. The present results are considered to be accurate within 0.3%; the precision error is much less than this.
TABLE I. SP~CIFIC H ~ A OF T ZIRCONIUM DIOXIDE T, K.
CP
T,OK.
CP
T,O K.
54.3 57.9 62.2 66.8 71.4 75.7 81.0 85.3 94.6 103,6
1.473 1.692 1.958 2.260 2.573 2 858 3.211 3.504 4 151 4 770
114.0 124.3 134.3 144.9 155.4 165.0 175.3 185.1 195.4 "205.1
5.471 6.154 6.761 7.399 8.016 8.542 9.057 9.537 10.03 10.44
215.0 225.2 235.7 245.5 255.6 265.9 276.1 285.8 295.0
C, 10.86 11.22 11.59 11.93 12.24 12.55 12.84 13.07 13.25
The entropy increment between 50.12' and 298.16' K., obtained by graphical integration under a plot of C, against log T, is 11,587 units. The entropy below 50.12' K. was obtained by 345 extrapolation. It was found that the function sum, D (7)
E
( y )+ (y), E
.- + I
adequately represents the measured spe-
cific-heat results over the entire experimentally determined range, where D and E denote, respectively, Debye and Einstein functions. This function sum was used in extrapolating to obtain 0.445 unit as the entropy increment between 0" and 50.12" K. In this instance the specific heat has decreased to such a low value at the lowest temperatures 12 i n v e s t i g a t e d that any method of extrapolation would yield virtually the 10 same result. The en3 tropy at 298.16' is the sum of the two portions or Soz~s.la = 12.03 * 0.08 calories per mole per degree.
8
L8 .I
j 6
u"
FREE ENERGY OF FORMATION AT 298.16'' K.
4
Bichowsky and R o s s i n i (1) a d o p t e d -258,100 calories per mole as the heat of formation of zirconium 50 150 250 T,OK. dioxide. The entropy of Figure 1. Specific Heat of formation, from the enZirconium Dioxide tropy value given above and those of the elements (4), is A S " 2 ~ 8 . 1 8 = -46.5. From the relation, AFO = AH" - TAS', A F " 2 ~ 8 . 1 ~= -244,200 calories per mole is computed as the free energy of formation of zirconium dioxide from the elements. 2
LlTERATURE CITED
(1) Biahowsky and Rossini, "Thermochemistry of Chemiaal Substances", New York, Reinhold Pub. Gorp., 1936. (2) Kelley, J. Am. Chern. Soo., 63,1137 (1941). (3) Kelley, U. 8.Bur. Mines, Bull. 371 (1934). (4) Ibid., 434 (1941). PUBLIEREID by permission of the Director, U. 5. Bureau of Mines.
