CORRESPONDENCE OF MOLECULAR STATES 219 



contained. This assumption is, of course, not valid 

 at high pressures. We also assumed that the mole- 

 cules of a gas do not form with each other systems 

 having potential energy, and hence that there are no 

 attractions or repulsions between them. 



If a body of gas for which there are no molecular 

 attractions is allowed to expand, as for example by 

 pushing a piston, it will do work at the expense of its 

 molecular k.e. of translation. Its temperature will 

 therefore fall. If it is then heated until its tem- 

 perature is restored it will require from the source of 

 the heat an amount of energy just equal to the external 

 work done in the expansion. But if no external work 

 is done during the expansion then no energy should be 

 required to maintain the temperature. Thus consider 

 two connecting vessels, A and B, which are separated 

 by a stopcock. Let A be filled with a gas at a high 

 pressure and let B be practically a vacuum. Let the 

 system be immersed in a vessel of water, changes in 

 the temperature of which may be observed by a sensitive 

 thermometer. After the temperature has become that 

 of the bath, the stopcock is opened. The gas rushing 

 from A into B does no external work. We should 

 therefore expect no change in the average k.e. and 

 hence no change in the temperature as indicated by 

 the thermometer. 



On the other hand, if the molecules form with each 

 other systems the potential energy of which increases 

 with their separation such an expansion involves an 

 increase in their p.e. This increase can be obtained 

 only at the expense of the kinetic energy of the mole- 

 cules. The temperature of the gas will then fall. 



