1207 



and E^ amounts to the melting energy or melting lieal ol n molecules B. 

 When the heat of melting of one molecule /? is indicated by Q, we get: 



E,^E,=znQ (1) 



When we ap[)lj the equation of Clapeyron Io the (wo three-phase 

 equilibria, (he indices 1 resp. 2 again referring to the equilibria 

 SSB(jr •■esp. SLG, the following relations follow: 



y.:^ = _^ and 7-1^' = A . . , . (2) 

 dT AK, dT AF, ^ ' 



in which Q^ and Q^ represent the heats of transformation. 



When Vs and Vl ai'e neglected with respect to Vq, which is 

 allowed, when the density of the gas phase is small with respect to 

 that of the other phases (pressure of the quadruple point C' smaller 

 than or in the neighbourhood of one atuios|)liere) and when the law 

 of Boyle is applied to the gas phase, we get: 



r_i=2:Lp^ and T —1 = -^ P^ . . . (3) 



dT RT ' dT RT ' ^ ' 



From this follows on iniegration on the assumption thai Q^ and 

 Qj are no functions of the temperature^): 



1) This assumption indicates that the algebraic sum of the specific heats (that 

 of the gas at constant 2wessure) of the substances participating in the transfor- 

 mation is zero. Tiiis is easily seen for the equiUbrium Uquid-gas on the following 



.,•.., • dQ Q 



consideration. From the equation of Clausius — — = h — H 4- 77, , in which h and 



H represent the specific heats of gas and Hquid along the boundary fine 



(VAN DER Waals — Kohnstamm. Thermodynamik. I. S 67') and from the equation 



rdP\ fdr \ dv 



h = Cv-YT[ - — , (Ibid. 1. S. 34. Gl. Ila; the index gr denotes that 



dTj„\dTj,j,. dT 



dQ rdP\ /dv\ Q 



is measured along the boundary line) follows ,>„ = Cv — H 4- T \ ( — + - • 



dT ^ ydTj,\d/rJ,,r T 



If the law of Boyle holds good for the gas phase, the two last terms of the 



second member of this equation can be replaced by R and we get — = — c/» — H. 



dT 



We derive in an analogous way that a similar formula also holds for the three- 

 phase equilibria described in the text. 



When the algebraic sum of the specific heats differs from zero, the integrated equa- 

 tion 4 may only be used for a small range of temperature ; then the heat of trans- 

 formation at the quadruple point must be calculated from the found value of Q. 

 A simular calculation follows in the discussion of the quantitative data. We may 

 point out in conclusion that if Q is no temperature function, the energy of trans- 

 formation, which is R2' smaller, does depend on the temperature. The variation 

 in £", caused by this correction is generally small with respect to the values of 

 Q and E. (See tables with the quantitative data in the following paper). 



78* 



