^2è 



that Planck's principle of finite elements of energy holds for each 

 principal mode of vibration of an oscillater whose motions can be 

 described by linear differential equations, whatever its constitution 

 may otherwise be. 



In this paper those consequences will be deduced for an ideal 

 monatomic gas. Similar applications of the quantum-theory to an 

 ideal monatomic gas were alreadj^ made bj' Tetrode ^) and by 

 Lenz"). Sackur^) also makes use of the quantum-theory for the 

 deduction of the equation of state, but in a different way. 



The deductions of Tetrode and of Lenz are based on the sup- 

 position that each principal mode of vibration of a gas enclosed in 

 a given vessel exchanges its energy by whole energy elements at 

 once. If this supposition is accepted it can be made probable by 

 contemplating the exchange of energy between the gas and the 

 radiation which is in equilibrium with it, that these energy elements 

 have a magnitude h ln\ v being the frequency of the (longitudinal) 

 waves in the gas, k the well known Planck's constant. The mean 

 "temperature energy" per mode of vibration is then found to be 



1 hv 

 , k being the well known constant of Boltzmann's entropy 



z 



kT - 

 e 1 



principle. 



As Prof. Kameri-ingh Onnes and I communicated to the Wolfskehl 



congress last month, this treatment gives results which do not conflict 



with observations on the equation of state of helium only '') on 



the condition that, in writing down the mean energy per mode of 



vibration for an ideal gas, a zero point energy to an amount of 



— hv is added to the above-mentioned expression for the temperature 



energy^). The same zero point energy was recently assumed for 



1) H. Tetrode. Physik. ZS. 14 (1913), p. 212. 



2) Gf. A. SoMMERFELD, Programme for the Wolfskehl lecture, Physik. ZS. 1 4 

 (1913), p. 262. 



3) 0. Sackur. Jaliresher. der Schles. Gesellschaft fur vaterl. Gullur, Febr. 1913. 



*) Viz. on the supposition that the determination of the frequencies of a gas in 

 a way corresponding to that which Debije fohows for a solid may be considered 

 as approximately correct. 



=; Hence the fundamental assumptions of this paper diverge from these of 

 Tetrode and of Lenz by the iulroduction of the zero point energy, from those 

 of Lenz moreover by the fact (§ 2), that for the magnitude of liie energy elements 

 i/o hr is accepted. 



