﻿of a Substance with Hydrostatic Pressure. 145 



we obtain 



f?7Ti 3 dir<L 



dt 



dt 



_ v 2 — vi dp l2 

 v* dt 



This gives an approximate value for the difference of 

 slopes of the two vapour-pressure curves. 



We will now show by a more precise treatment, in which 

 proper allowance is made for the variation of vapour-pressure 

 with hydrostatic pressure, that this equation is not approxi- 

 mate merely, but exact when certain exact meanings are 



given to -jf- and — ^ . 

 6 dt dt 



The hydrostatic pressure may be imagined to be applied 

 by means of a permanent gas placed in the vapour chamber. 

 It is much better, however, if we make use instead of a semi- 

 permeable membrane which separates the liquid and vapour 



Fig. 1. 



P wl Licjcnd 



Va|x>c 



A " B 



one from the other ; so that, if the membrane is permeable 

 to the vapour alone, any pressure whatever, p, may be 

 imposed on the liquid, and the vapour will then be able to 

 take up the vapour-pressure ir p which corresponds to this 

 hydrostatic pressure. With such an arrangement, shown 

 more in detail in fig. 1, a cycle of operations can be made, 

 each reversible in character, and the mechanical efficiency of 



this cycle may be given its universal value tjt« 



In estimating the work done during the cycle we note 

 that this is given directly as the sum of all such values as 

 ^pdv for its various stages. Great simplification is brought 

 about, however, if use be made of the facts that 



£2 £2 



\ pdv=p 2 v 2 —piVi*-\ vdp always; 



and that for any cycle of operations the sum of all the values 

 of j} 2 t) 2 -^i is necessarily zero, and therefore the work 

 done is given by the sum of all the values of —^vdp. 



Imagine then a four-stage cycle performed, and estimate 

 Phil Mao. S. 6. Vol. 29. No 169, Jan. 1915. L 



