BRIDGMAN. — THERMODYNAMIC PROPERTIES OF LIQUIDS. 103 



particular arrangement which the molecules adopt, and the relation 

 of the local centers of force to this arrangement, it is conceivable that 

 the potential of the attractive forces should be either greater or less 

 at the lower temperatures and equal volumes. The likelihood is, 

 however, that the potential will usually be less at the lower tempera- 

 tures. Similarly, it is usually more likely that the potential of the 

 attractive forces should be less at the higher pressures. As a rule, then, 

 an increase of temperature of one degree at a higher pressure or a 

 lower temperature must provide the energy to do more work against 

 the attractive forces, so that the specific heat at constant volume 

 will be greater at higher pressure and lower temperature. But in 

 those more infrequent cases wdiere the potential energy of position 

 is less at the higher temperature or lower pressure, the specific heat 

 will be less at higher pressures and lower temperatures. It is as a 

 rule true, as we have seen from the curves, that C^ does become 

 greater at the higher pressures and lower temperatures. 



The considerations just discussed are somewhat similar to consider- 

 ations regarding the association of the molecules, but do not in all 

 cases lead to the same results. For instance, if we suppose a liquid 

 of single molecules to associate to one of double molecules, the specific 

 heat of the associated liquid would be one half that of the simple one, 

 if we neglect the effect of the altered number of internal degrees of 

 freedom. 



The second hypothesis made above, that a given increase of temper- 

 ature always corresponds to the same increase of molecular energy, 

 probably breaks down also at high pressures. The difficulty of de- 

 termining what happens in this case is increased by uncertainty as to 

 what the definition of temperature shall be at high pressures. We 

 may perhaps, however, think of temperature at low pressures as being 

 roughly proportional to the a\erage translational energy of the 

 molecule during its free flight. Now we have seen that as pressure 

 increases, the time of free flight decreases rapidly, and an increasing 

 fraction of the time is spent in collision. During collision the kinetic 

 energy of translation has become potential within the molecule. The 

 result is that as pressure increases, the potential strain energy of the 

 molecules becomes a greater part of the total energy, leaving a smaller 

 residue to become kinetic. Now if temperature corresponds to 

 translational kinetic energy, it is evident that at high pressures more 

 total energy must be imparted to the substance to increase the trans- 

 lational energy a given amount, or in other words, the specific heat 

 will increase with increasing pressure. 



