X,>P,^,AND THE CRITERIA OF EQUILIBRIUM 223 

 and 



tdt] = de + pdv, 

 it follows in the usual way that 



dx = tdr] + vdp, 

 whence 



5. Physical Properties of the Thermodynamic Functions \j/, f , x- 

 Gibbs' statement about these may be paraphrased and extended 

 as follows (Gibbs, I, 89, 92). 



If AQ represents the heat communicated to any system 

 during any process in which the external work performed is 

 ATT, we know always that 



AQ = Ae + ATF. 



Further, for any infinitesimal reversible change in which the 

 masses of the ultimate constituents of the phase are unchanged, 



t 



dQ = tdt], 



6. The Heat Function at Constant Pressure. Let the system 

 undergo a change at constant pressure, in such a way that the 

 only external work done is work of expansion. Then 



ATT = pAv, 



