53 MOLECULAR AND ATOMIC ENERGY 119 



In this form the proof is bound up, as was before 

 mentioned, with the assumption that the gas obeys the ideal 

 gaseous laws, and especially that its specific heat c at constant 

 volume does not alter with the temperature. We can, how- 

 ever, easily free ourselves from this assumption and establish 

 a more general formula, which serves also for the case 

 wherein the specific heat does vary with the temperature. 



If , are two temperatures between which the value 

 of the specific heat may be taken constant, the formula 



H - H Q = Jcp(S - @ ) 



gives the whole amount of energy which must be added 

 to unit volume of the gas to heat it from (B> to <B) without 

 expansion. The kinetic energy of the molecular motion 

 thereby simultaneously increases by 



where p p is the resulting increase of pressure. Since 

 for this change of pressure the relation 



holds good, we have the more general formula 



H-H~ 2 c 



the interpretation of which is quite similar. 



54. Monatomic Molecules 



To prove whether or not this theoretical formula corre- 

 sponds to the truth, we may apply it to the special case of a 

 gas whose molecules consist each of a single atom. To this 

 class of gases, which we may call monatomic, if we may use 

 this word in a different sense from the term single-valued, 

 belong the vapours of mercury, cadmium, and perhaps zinc. 

 For these monatomic vapours the possibility of assuming 

 proper motions of the atoms, in addition to the motion of 

 the molecules, falls to the ground ; we shall therefore have 

 to suppose that in these vapours the kinetic energy K is 

 identical with the total energy H, provided that, like gases, 

 they may be considered free from cohesion. 



