178 Mr. W. Sutherland on the 



there it acquires the temperature which it had on the high- 

 pressure side. The escaping gas does work p 2 v 2 on the 

 atmosphere, but at the same time it has work p x Vi done on it 

 by the gas behind, so that p 2 v 2 —p\Vi i s the total external 

 work done by the gas ; but the gas also gains potential 

 energy by expansion, so that the total loss of kinetic energy 

 is equal to the sum of these two quantities. But K p 8 is the 

 quantity of energy which has to be given to the gas after its 

 loss of kinetic energy to bring its temperature back to what 

 it was on the- high-pressure side. Now, if the temperature of 

 a body were a function of only the kinetic energy of its 

 molecules, we could say that K^S is the change of the kinetic 

 energy of a kilogramme of gas on account of the expansion ; 

 but the characteristic equation shows that temperature is not 

 a function of only the kinetic energy, for it asserts that the 

 kinetic energy of translation of the molecules in a kilogramme 



q — 



is ~(ae v ^~\ — \T, whence we see that we cannot consider 



K P S as giving accurately the total change of kinetic energy 

 due to the performance of external work and the gain of 

 potential energy. But if from K^S we subtract p 2 v 2 — P\V\, 

 we shall get a remainder depending for the most part on the 

 change of potential energy due to expansion. If, then, we 

 bear in mind the values already given for the constants of the 

 characteristic equation, and the value '7 for A, we see from 

 the last equation above that the greater part of the said 



remainder arises from the term 1 1 ), which, according 



to the molecular theory, expresses the change of molecular 

 potential energy. The term «A log — is small in com- 

 parison with 1 1 j ; but its meaning is very important, 



as it is bound up with the difficult question of the dynamical 

 explanation of the second law of thermodynamics. The term 



Ac I ) may be taken with a A log — , but it is really 



\i>! V v i 



negligible ; while the last term, a J - Y neglecting A 



in the numerator, arises from the fact that the relation between 

 the kinetic energy of the molecules of a gas and its temperature 

 involves the volume occupied, and therefore varies with ex- 

 pansion. In fact, = ( ) represents a heating- effect 



