LEWIS. — FREE ENERGY AND EQUILIBRIUM. 17 



and any formula that is universally applicable to one state must also be 

 applicable to the other. Thus all the equations already developed for 

 gases apply without change to simple liquids (having a constant molecu- 

 lar weight) under the restrictions already mentioned, namely, that in the 



equations 



RT rfm , RT a 



■2 ' 



v—f{i-) dv ^ v — b V 



—z — and — ; are independent of the temperature only when -~ = 0, 



that a has not been proved to be a constant in all cases but may be a 

 function of the volume, and that b is not necessarily a constant with 

 changing volume, although it is in all cases independent of the temper- 

 ature. 



Regarding the question of the variability of c^ with the volume in the 

 case of liquids we have no direct experimental evidence, but indirectly it 

 can be shown that c„ is practically constant, for Ramsay and Young 

 (page 14) found that equation (25), p = A T — B, applies to liquids 



dc 

 as well as to gases, and this equation can only be true when — ^ = 0.* 



dv 



dc 

 If —r^ is not equal to zero, then the general equation (8) must be 



used, 



RT d^ dm^^ r-^i dc; 



this, differentiated with respect to T, v constant, gives 



dp _R d^ d'wi , ri dc, ,^ , dc. 





+ / -— vr-f 



dT V dv dv dT ' J T,T dv ^ dv 



„. d-Wi. dc^ „ , ^^^ 



oince -z 777,= T — from equation (9), 



dv dr dv ^ ^ 



^^^R_m+ rL,p,r=c+rp'-i, (29) 



d 1 V dv J T^T dv J T^dv T ^ ^ 



where C is a constant; while from equation (25) ~rL= ^• 



Notwithstanding this evidence for the approximate constancy of the 

 specific heat, the experimental work of Joly f on this subject seems to 



* Compare Nernst, Theor. Chem., p. 202, 



t Phil. Trans. Roy. Soc, 182A, 73; Proc. Eoy. Soc , XLVII. 218; LV. 390. 



VOL. XXXV. 2 



