FUNDAMENTAL EQUATIONS OF IDEAL GASES 351 



from which the vapor pressure equation was obtained above. 

 Gibbs preferred to proceed directly with the /x equations in 

 estabhshing his vapor pressure relation. 



It will be noted that Gibbs has assumed that the heat capac- 

 ity k of the liquid is independent of the temperature. In 

 addition it is assumed that the internal energy is a constant. 

 It is in this way that the simple expression for the entropy 

 1] = log t -\- H' is obtained. These assumptions are, however, 

 far from being true if a range of temperature is considered, as a 

 glance at the data for the heat capacities of liquids shows. As 

 compared with the vapor at moderate pressures most of the 

 internal energy of a liquid is molecular potential energy and 



f ( — ■ ) — p is very large. Ether, for example, at — 50 has a 

 \ot/v 



/dp\ 

 specific volume of 1.265c.c.per gm., and t{—j ~ p, equivalent 



to ( — 1 , amounts to 2780 atmospheres. The same quantity 



for the vapor in equilibrium with the liquid at — 50 is not far 

 from 1.5 X 10~^ atm. For short ranges of temperature along 

 the saturation curve the Gibbs' assumption is in many cases 

 admissible where only modest accuracy is required. The 

 subject of vapor pressure representations on the lines of Gibbs' 

 treatment has recently been fully developed by L. J. Gillespie.^^ 



It is worth pointing out that Gibbs' treatment indicates 

 the role played by the entropy constants in the constant of the 

 vapor pressure relation. The heat theorem of Nernst is also 

 closely related to the constants of the vapor pressure-tem- 

 perature equation. To obtain, however, constants which are 

 really characteristic of pure substances requires very reliable 

 data at low pressures and skillful treatment of the data in 

 formulating an equation ^"^ ^^' ^^^ ^^' ^^- ^^ 



The treatment of the case where a gas is dissolved in a 

 liquid is also touched upon by Gibbs in the latter part of the 

 footnote. It is assumed that the vapor pressure of the liquid 

 absorbing the gas is small enough to be neglected. However, 

 while the latter approximation may be satisfactory, as for 

 example with carbon dioxide at one atmosphere dissolving in 



