102 PROCEEDINGS OF THE AMERICAN ACADEMY. 



The curves are the same in general character as those for Cp. The 

 differences consist in displacements of the pressures of maximum or 

 mimimum, or occasionally in the suppression of small irregularities; 

 but the larger features are the same. The curves for the four normal 

 alcohols retain the same resemblances as before, and isobutyl alcohol 

 is as strikingly not a member of the series. Isobutyl alcohol and ether 

 show general resemblances as to the specific heat, which may, however, 

 be accidental. The halogens are also different from the other liquids 

 with respect to Cj. 



The importance of tabulating C^ is that it is a quantity of much 

 greater simplicity than Cp. When we determine Cp by heating the 

 liquid at constant pressure, the liquid expands with rising tempera- 

 ture, and in so doing performs work against both the external pressure 

 and the internal attractive forces. Cp is greater than C„ by this 

 work against external and internal forces. Consequently, it is 

 usual to tacitly assume that C„ contains only the work necessary to 

 raise the temperature energy of the molecules. Evidently the assump- 

 tion is merely another way of stating the assumption that the poten- 

 tial energy of the attractive forces is a function of the volume only. 

 Furthermore, it is usually assumed in discussions of the significance 

 of Cj that a given increase of temperature corresponds to a given 

 increase of kinetic energy of the molecule, no matter what the pressure 

 of the liquid. It is true that when the kinetic energy of the molecule 

 is to be raised, more total energy must be imparted to the molecule 

 than just sufficient to increase the kinetic energy by this amount, 

 because of the law of the equipartition of energy among the various 

 degrees of freedom, but if the degrees of freedom remain unaltered, 

 we still have the result that to increase the temperature by a given 

 amount requires the same amount of work independent of the volume. 

 The consequence of the hypothesis would be that the specific heat at 

 constant volume is independent of pressure and temperature. 



Figure 112 for the average C^ of the twelve liquids, shows that even 

 on the average C^ cannot be independent of pressure, and the preced- 

 ing diagrams for the separate liquid show that it certainly cannot be 

 independent of temperature. In general the behavior of C^ seems 

 to be at first a decrease, and then with increasing pressure an increase 

 again. Probably the reason is that neither of the simple hypotheses 

 which we discussed above are valid for high pressures. We have 

 seen that at high pressures we m'ay expect the molecules to approach 

 positions of more or less regularity of arrangement, and that the 

 regularity is greater at the low temperatures. Now according to the 



