gained during the Mixing of Gasts. 315 



into the reservoir. The effect of this series of operations is nil, 

 and there can be neither gain nor loss of work. The work gained 

 in the first operation is consumed in the four h, since pv^Yv , 

 so that attention may be confined to the second and third opera- 

 tions. Now the work consumed in the compression from v to 

 is 



\ pdv = Pv \ -? = Vv log ~= Pi> log 



and the work gained in the descent 



And these are equal, since 



. P 



so that on the whole no work is lost or gained. 



The case is different when there are two kinds of gases pre- 

 sent. Although, as before, the work gained in the first opera- 

 tion is consumed in the fourth, there is no longer compensa- 

 tion in the second and third operations. If P x and P 2 are the 

 partial pressures in the reservoir, the work required for the com- 

 pression from v to v is 



On the other hand, the work gained in the descent is 



9 sv o\Y + ^)=^<MQi + ^2Q 2 )> 



if Qi, Qg are the partial pressures of the abstracted gas after 

 condensation to volume v Q . Thus, on the whole, if W be the 

 work done on the gases, since Qi+Q2=Pi + P 2 > 



— =Q 1 (log^-^ + (^(log^-/x 2 A 



Now/j^P^""^*, and v j /9 1 = v Q 1 ; so that 



vPje-'^VoQ,. 

 Accordingly 



log ^ ~^ Z= log (^ 6+w *) "^ Z=S log §/ 



Similarly 



lo S,r-/V=l°grr; 



and thus 



W = Cu {Q 1 log|' + Q s log^} (3) 



Y2 



