670 



Probably even the compensation lefei-red to above already takes 

 place in tlie ideal gas state, at least if the volume of the mixtnre 

 is not increased at too rapid a rate to oo as the temperature de- 

 creases to 0. 



In accordance with a remark by Nernst ^) we are practically 

 forced to assume that for the molecular translatory motion of a 

 gas on approaching to T=n:0 at last the equipartition laws are no 

 more valid. For the determinalion of the temperature one can then 

 no more rely u])on the gasthermometer. A method for the deter- 

 mination of the temperature, which is then suitable in theory, is 

 this that one derives the temperature from the energy density of the 

 radiation which is in eqnilibrium with it. 



We shall consider tlie e(|uilibrium between the molecular translatory 

 motion of the gas and the radiation subsequently at two temperatures 

 Tand T-{-dT. The most obvious assumption is that to an increase 

 of the energy density of the gas an increase of the energy density 

 of the radiation corresponds which is in a finite ratio to the first, 

 in other words that 



dU=yT'dT, (2) 



where y has a finite, and at sufficiently low temperature a constant 

 value. In this equation U may represent the energy of the gramme- 

 molecule of the gas. The molecular volume is supposed not to 

 become oo on approaching to T^O. 



From (2) follows that') 



f- ^=' ^ ijfjr' <'' 



The equation (2) has the same form as the corresponding relation 

 for a solid. Indeed it could hardly be assumed that the equilibrium 

 between the molecular motion of the gas molecules in colliding 

 against a solid and the radiation w^ould be governed by quite a 

 different law from the equilibrium between the molecular motion in 

 a solid and the radiation. 



From (2) and 



^=1?. >« 



') W. Nernst, Physik. Z.S. 13 (1912), p. 1066. Gf. also H. Kamerlfngh Onnes 

 and W. H. Keesom, Math. Enz. V 10, Leiden Gomm. Suppl. N». 23, note 517. 



') It will be noticed lliat for the validity of (3) a decrease of I ^, I proportion- 

 ally to T^, as is indicated by (2), is not required, but that a derrease proportionally 

 to 2' would be sufficient. 



