BRIDGMAN. THERMODYNAMIC PROPERTIES OF LIQUIDS. 97 



tion of curvature was in each case such as to suggest that this decrease 

 might not continue indefinitely, and it was suggested then that there 

 must ultimately be a reversal of the effect. It seemed surprising 

 that at pressures as high as 12000 kgm. the attractive forces should 

 still do more work than could be stored up as strain by the external 

 forces. 



Figure 85, giving the average for the twelve liquids, shows that the 

 anticipation of a reversal in the change of energy is justified for nearly 

 all the liquids; that is, the internal energy, after decreasing for a 

 while, passes through a minimum (on the curves a maximum) and 

 from here increases with rising pressure. The necessary existence of 

 this maximum could of course have been predicted from the curves 

 for the heat and the work of compression, since the one is either 

 linear or concave upwards, while the other is concave downwards. 



The change of energy is markedly different for the different liquids, 

 whereas the other thermodynamic properties are similar. Of course 

 the reason is that we are here concerned with the difference of two 

 effects. The position of the maximum of the difference of two func- 

 tions is very sensitive to slight changes in the functions themselves. 

 Under these circumstances, the mere existence of a maximum is evi- 

 dence of similarity. The only curves which do not show the maxi- 

 mum are methyl and propyl alcohol. It will be remembered that 

 the work of compression curve for methyl alcohol had a reversed 

 curvature at the upper end, and that the work of compression of 

 propyl alcohol was abnormally low. 



It is of interest to plot the change of energy against volume, because 

 it may give information about the attractive forces. If the attractive 

 forces are central forces, functions only of the distance from the 

 centers of the molecules, then the potential energy of the attractive 

 forces will be a function of the volume. Thus if the attractive forces 

 are proportional to the inverse fifth power, as has often been supposed, 

 then the potential energy is inversely as the fourth power of the 

 distance apart of the molecules, or as the inverse four thirds power 

 of the volume. This relation was tried for four of the twehe liciuids; 

 for amyl alcohol, ether, phosphorus trichloride, and ethyl iodide. 

 The change of internal energy of these liquids was plotted against 

 V~^. The diagram was the same in character as the diagram plotting 

 the change of energy against V, except of course that small values of 

 V~^ correspond to large values of V. Now if the change of internal 

 energy is proportional to Vq~^-V~^, this curve plotted against 

 F~* should be linear. The curves were verv nearly linear in the in- 



