amongst the Molecules of a Gas. 91 



p A denoting the density of the gas A when its a molecules 

 are distributed through a volume V 2 . 



Then for the increase of potential due to expansion we have 



Aam(p A -p A )+Bbm'(p B -p Bi ) + 2C \/AB bm'(p A -p A ). 



Now the last term in this has the same value as 



2C </ABam(p B -p B ); 



so that it may be replaced by the square root of the pro- 

 duct of the two, namely 



20 v/AB am bm {p B -p B )( PA2 -p A ). 



Hence for the increase of potential energy we have the 

 sum of the two expressions Aam(p A —p A ) ; Bbm'(p B —p B ) ; 

 and C times twice the product of their square roots. 



Now suppose that Y 1 is the volume of the mixture at a 



pressure P x ; V 2 at a pressure P 2 ; the temperature T being 



the same in each case. Then p A is to the density of the gas A 



. "V 

 at pressure Pj in the ratio —^ and p A is to the density of 



.V 



the gas A at pressure P 2 in the ratio — ^a, which is equal to 



* 2 



the previous ratio. Thus the term Aam(p A —p A ) may be 



written 



Y 

 Aam^i(p' A -p A ), 



where p A p A represent the densities of A at pressures P x and P 2 - 



! v 



But this is — ^i times the gain of potential of a mass am of 



the gas A escaping from underpressure P 2 to pressure P^ or, 

 if we call 6 A the cooling effect for A corresponding to P 2 — P 1? 

 we may write it 



where s A is the specific heat of A. 



For the other terms in the gain of potential by the mixed 

 gases we can write corresponding expressions, and get for 

 the result, 



To obtain the cooling effect corresponding to this we must 

 first divide by J, and then by the thermal capacity of the 



