ae 
Diffusion in Solution of Dissociated Gases. 269 
1 ‘ 1 
(P, — 2g pa )Vi= (P: + “ P2)Vo= RO. 
The work done by the gas in this part of the operation is 
evidently 
gk 
(P; +p) Vi- (P, + po) Ve = — (piVy —p2V2). 
‘The rest of the eycle consists merely in isolating a volume 
V, of the gas at pressure P, + p, and expanding it isothermally 
at 6° till its pressure and volume become P,+>p, and Vy, 
respectively. 
It is evident that we have now carried out a cycle at 
constant temperature which is perfectly reversible at every 
stage. We may therefore independently equate to zero the 
external work done, and the total heat absorbed, by the 
system. Onaccount of the complicated nature of the integrals 
which arise in the general case, the calculation of the work 
done during the expansion from volume V, to V, aime 
has only been carried out in the case where the pressure (7) 
of the dissociated gas is small compared with that (P) of 
the undissociated. The work done in this part of the cycle 
is evidently | 
*¥5 
{ *(P+p)aV, 
wv V, 
where the relation between P, p, and V is given by the 
modified gas equation above, together with the law of dis- 
sociation 
1 we ' 
prlky=P+ p(=P approximately). 
7 
To this approximation 

= oe = 
p=(ho Py — V yr , 
When the above aes is Meo ag on this basis we obtain 
RO logy ts » (éRO)» a a eel As mae ), 
Adding this to the — done in the previous part of the 
cycle and equating the sum to zero, we obtain the ale 
equation to determine the relation between V, and V,: 

1 1 a—} 1 pxV2 
Bs ee ae ee 
V; er no ra oe 
5 er E ne Ae 
‘ ~ eg” a, ae a ad 
Phil. Mag. 8. 6. Vol. 7. No. 39. March 1904. U 
