﻿104 Mr. D. Tyrer on the 



W represents total work done against molecular attraction 

 during the expansion of the liquid. Integrating, we have 



w=c(~ J-A (1 



where 0= . % t - T ^ 7l V and is a constant dependent only 



on the nature of the liquid. In deducing this equation for 

 the isothermal change of potential energy of an expanding 

 liquid, the usually accepted assumptions in regard to mole- 

 cular energy have been made. On account of their importance 

 in the later portion of this paper these assumptions may be 

 stated here. 



(1) The kinetic energy of the molecules of a liquid or gas 

 is independent of the volume. 



(2) When a liquid expands isothermally, the energy ab- 

 sorbed goes entirely to do (a) work of expansion against 

 molecular attraction, and (/>) work of expansion against an 

 external pressure. 



(3) The total attraction exercised by a group of molecules 

 on a single external molecule a certain distance away is the 

 sum of the attractions exercised by each of the molecules 

 separately. 



Jf V 3 and V 2 are the volumes of the liquid before and after 

 expansion, and if work is also done against an external 

 pressure p = <f)(Y) which varies from ■p 1 = cj)(V 1 ) to j> 2 = $(V 2 ), 

 equation (1) becomes 



W, is V 2 3 S J Xl 



(2) 



where S ha3 been put equal to V T . 



If we consider the case of the expansion of a liquid to the 

 state of vapour, equation (2) becomes 



L=C/-4n--i ri WE, .... (3) 



/J _!_Ue 



n-l T »-i T-^J 



where L is the latent heat of vaporization, V L and Y v are the 

 specific volumes of liquid and saturated vapour respectively, 

 and E is the external work done during the vaporization. 

 Now we might apply this equation to the determination of n 

 by substituting for L, E, V x and Y v their values at different 

 temperatures for a given liquid ; but the value of n thus 

 obtained would not necessarily be the true value. For 

 example, when n is put equal to 2 or 7, two equations are 

 obtained both of which fit the facts equally well *. But if 

 * Vide Kleeraan, Phil. Mag. Jan. 1911, p. 83. 



