354 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



expect from the ordinary theoretical considerations, however. It is 

 usually considered that when the volume of a substance is kept in- 

 variable all, or else a fixed fraction, of the heat put in during a rise of 

 temperature goes toward increasing the kinetic energy of the mole- 

 cules. This is because the temperature is supposed to be proportional 



105 LOO .95 .90 .85 



Volume, cm.^ per gm. 



Figure 13. The specific heat at constant volume of water as a function of 

 the volume, 



to the energy of translation of the molecules, and therefore, because 

 of the law of the equipartition of energy, to the total energy of the 

 molecules. We should expect, therefore, that the input of energy 

 required to raise the temperature by a specified amount would in- 

 volve only the interval of temperature, and would be independent 

 of the absolute value of the temperature and of the volume. The 

 curves show most convincingly that this is not the case. This sug- 

 gests that in formulating a theory of liquids it would be well to 

 scrutinize pretty carefully several assumptions that underlie the 

 above considerations, namely that the temperature is proportional to 

 the kinetic energy, that a fixed fraction of the total energy of the 

 molecules is kinetic, and that the law of the distribution of velocities 

 is independent of temperature. 



Another quantity of thermodynamic interest which may be found 

 in terms of the specific heats is the thermal effect of compression, 

 that is the rise of temperature in degrees accompanying a change of 

 pressure adiabatically of one kgm. per sq. cm. This may be computed 



fdv\ 



/dT\ "^UrJ 



by the thermodynamic formula ( -^ ) = -\z — ~. The results so 



\dpJ^ Cp 



