MECHANICAL EQUIVALENT OP PRESSURE MARGULES 523 



therefore no work done along the remaining portions P 2 p 2 and 

 p l P x of the whole circuit. Hence the quantity of heat q is the 

 equivalent of the total work done along the horizontal portions 

 of this circulation. 



Since byyintroducing the equation for adiabatic change of con- 

 dition we obtain 



r 1 r 1 -rlT;-r 1 r I (£V A7,> 



Pl 



therefore for i kilogram the total change of entropy or the sum of 

 the changes during one circulation is 



J r, T J t 2 ' T p S T[ x 2 



This cycle is reversible. If during the upper path the air is forced 

 against the gradient, then we have to add as much heat as was 

 withdrawn in the above-described direct cycle, and similarly in 

 the lower path we must abstract heat instead of adding it. The 

 work done against the pressural force is converted into heat and 

 the difference of pressure remains unchanged. 



The useful effect or efficiency of the heat added in the former 

 direct cycle is very nearly equal to 



1 ^2+^1 



n + t 2 



and it increases with the difference of level of the upper and lower 

 horizontal paths. 



(8.) STEADY CIRCULATION IN MOIST ATMOSPHERE 



A cycle with additions of heat varied so as to imitate the process 

 in moist air may be constructed in the following manner: 



In the preceding scheme let aqueous vapor be added at P 2 and 

 let the mixture of air and vapor ascend so high that at p 2 the vapor 

 has nearly disappeared. The water condensed in each elementary 

 portion of the path P 2 p 2 is assumed to fall away immediately and 

 be collected again at P 2 . In this case using one cycle the addition 

 of heat to one kilogram of dry air is not only the quantity needed 



