FUNDAMENTAL EQUATIONS OF IDEAL GASES 349 



77 — mH a 



X = mE + mic + a)e ""^^^ ( ?Y~", (21) 



mH 



/dx\ _ »"(= + «) /p\ 



ma 



7' 



(22) 



but 



1]— mH 



e (2) =Z7rT^.=<, (23) 



which gives 



( 



m{c + a) 

 dx\ fnat 



dP/r,, m V 



= V. (24) 



It is also easily shown that ( ~ ) = t, while { ~- ) gives 



an equation for /x identical with [268], 



13. Vapor Pressures of Liquids and Solids. The footnote 

 (Gibbs, I, 152) concerning the general problem of vapor pres- 

 sures is important, for not only is a relation between pressure 

 and temperature often required for pure liquids or solutions in 

 equilibrium with a vapor phase, but equally important is the 

 large class of compounds of solids with volatile components, as 

 for example the salt hydrates, salt compounds with ammonia, 

 sulphur dioxide, and numerous similar compounds. Innu- 

 merable formulae for the vapor pressure of liquids have been 

 suggested since the middle of the last century. Those that do 

 not have a purely empirical origin may be obtained from the 

 Clapeyron equation 



dp 



using various assumptions. Thus if the specific volume of the 

 liquid Vo is neglected, the vapor, Vi assumed a perfect gas, and 

 the heat of evaporation, X supposed a linear function of the 

 temperature, there results 



dp at , ^ 



Xo + a< = i ir • -' (25) 



at p 



