52 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



this vapor alone. A change of temperature will change the vapor pres- 

 sure in A B without changing the total pressure on the liquid, which 

 is always equal to the outside pressure on F. We may simplify this 

 arrangement by making the layer of inert gas so thin that it may be 

 regarded together with the membrane B C merely as a single membrane, 

 which is impermeable to the liquid but permeable to the vapor. In 



A 

 C 



D 



5 



Figure 1. 



Figure 2. 



Figure 2 it is represented by the dotted line B. The spaces B C and A B 

 are filled with liquid and vapor respectively, and the pistons A and C can 

 be moved up and down so as to distribute the substance between the 

 liquid and gaseous phases as desired. The whole is removed from the 

 influence of gravity. Let us start with one gram-molecule of the sub- 

 stance, all in the liquid state, and pass through the following reversible 

 cycle, during which the pressure, P, upon the piston, C, remains constant, 

 while the pressure upon A is always kept equal to the vapor pressure. 

 At first the piston A is at B ; the space B C has the volume v 2 . (1) The 

 temperature is raised from T to T + d T, the pressure on A being raised 

 at the same time from p, the original vapor pressure, to p + dp, so that 

 none of the liquid evaporates. The piston C moves down on account of 

 the expansion, dv 2 , of the liquid. (2) All the liquid is evaporated at 

 temperature T -f d T, C moving to B, and A moving up to furnish the 

 volume, v v (3) The temperature is again brought to T; the pressure 

 on A to p. A moves down on account of the contraction di\. (4) All 

 the vapor is condensed and the original condition is restored. The 

 amounts of work done by the system in the several steps are : — 



W l = Pdv 2 , 



W 2 = -P(v 2 + dv 2 ) + (p + dp) Oi + dvj, 



W 3 = — p dv u 



Wi = Pv 2 — pv v 



