226 MILNE 



ART. F 



or 



/ 



^X = j Cpdt. 



It follows that in the adiabatic rectilinear flow of a perfect gas 

 from rest at temperature ^o to motion with velocity q at tem- 

 perature t, we have 



h Q^ = — Cpdt. 



J to 



The above somewhat miscellaneous calculations serve to illus- 

 trate the properties of the heat function. 



8. The Work Function \p at Constant Temperature. Let the 

 system undergo a change at constant temperature, doing ex- 

 ternal work in any way whatever (e.g., electrically), as well as by 

 expansion against external pressure. Then 



A\P = A(e - tri) 



= Ae — tAr{, 

 and as usual 



AQ = Ae + AW. 

 If the change is reversible, AQ = tArj, and so in this case 



A;/' = -AW, 



or the increase in the work function is equal to the negative of 

 the external work performed. (Gibbs, I, 89, equation [110].) 

 Hence the name "work function." 



All reversible processes connecting two states of the same 

 temperature yield the same amount of external work, and any 

 irreversible process connecting them yields less work. Thus 

 the decrease in the work function gives the maximum amount 

 of external work obtainable in changing from the first to the 

 second state. We can prove this in another way, from first 

 principles, as follows. If A'Q is the heat absorbed in any change 

 whatever, by Clausius' inequalities we have 



A'Q 



At; ^ 



t ' 



