256 WORK OF EXPANSTON OF STEAM. 



from a cubic foot of water.* Since the volume is always a 

 function of the pressure, we may write 



V=f(P). (I) 



136. Work of Expansion of Steam. Let V be the 



volume of steam from a cubic foot of water at the pressure 

 P, where P is the pressure on a square foot, and Uq the 

 work performed by Q cubic feet of water, in the form of 

 steam, between the pressures P and P t ; 

 let ABCD be a vertical section of the \ 



space in which the steam expands, ^~ ~~7t 



ABPQ the volume V of the steam at the N\ , fa 

 pressure P, ABPjQj the volume F t of \ I 



the steam at pressure P 1} A the area of F i g . 69 



the section at PQ in feet, and dv the dis- 

 tance between the two consecutive sections PQ, and MN. 

 Then, for the element of work performed by one cubic foot 

 of water in the form of steam at the pressure P, we have 



dU^ = APdv = PdV, 



since Adv = dV. Integrating between the limits P and 

 P x , we have 



Vi=f*rw=f p P pdf ( p) (i) 



[from (1) of Art. 135]. 



Therefore, for the work done by Q cubic feet of water in 

 expanding from P to P 1? we have 



Uq = Qf*Pdf(P), (2) 



which can be integrated when the function /(P) is known. 



Sen. Since from (2) the quantity of work done is en- 

 tirely independent of the form of the vessel ABCD, it 



* See Eucy. Brit,, Art, Steqm.^ 



