amongst the Molecules of a Gas. 93 



effects in different mixtures and see whether they agree ; that 

 is, whether our theory can be tested by its power to explain 

 with any exactness a very peculiar experimental fact. 



There are no systematized experimental results by means 

 of which the value of pv for different mixtures of air and C0 2 

 at different temperatures could be obtained directly ; but the 

 following argument will show that we can make use of our 

 previous numbers for the values ofpv—p'v' at different tem- 

 peratures in the case of air and C0 2 , to deduce the numbers for 

 any mixture of air and C0 2 at the same temperatures. Let V x 

 be the volume of a mixture of the two gases at a certain tempera- 

 ture and a pressure T l ; as before, let Y A , V B be the volumes 

 which the constituent gases in Vi would occupy if separated 

 at pressure P-^ Let W 1 be the potential energy of the mixed 

 gases W A , W B of the two separated gases ; then actually to 

 separate the two gases will require work, 



Wi _ Wa _w e . 



Expand the separated gases to a condition represented by 

 suffix 2, just as they were expanded in Thomson and Joule's 

 experiments, that is without doing external work other than 

 that corresponding to the values oipv—p'v r for each gas ; thus 

 each of the separated gases would be cooled by the amount 



7JV — T) V 1 



— — j- — previously calculated, and each would be cooled by 



its respective amount 6 A or B , on account of the separation 

 of molecules ; so that altogether the gain of potential energy 

 during the expansion will be the sum of Js A 6 A and Js B # B and 

 the two corrections pv — p f v'. Thirdly, allow the gases to 

 diffuse into one another. In this case the work required 

 will be 



_-w 2 +w Ai +w B , 



Hence the total gain of potential energy by the mixed gases 

 on expanding from volume Y 1 to V 2 is 



Wl _w A -w B -w 2 +w Aj +w B!+ j,A+Jv>B 



+ (PiV Ai -P 1 V i ,) + (P 1 V B -P 2 V Bj ) ; 

 bat W A -W A =J S ^ A ; W b -W b =J Sb b . 



So that the total gain reduces to 



W I -W s + (P 1 V A -P 2 V As ) + (P 1 V Bi ^P 2 V B ), 



and this corresponds to the total actual cooling effect observed 

 by Thomson and Joule. The cooling effect denoted above by 

 6 is the equivalent of W A — W 2 ; to obtain 6 then from the 



