229 



tlie molecular rotations by Einstein and Stern ^) for the explanation 

 of tlie behaviour of the specific heat of hydrogen. 



The supposition of a zero point energy corresponds to the newest 

 ideas of Planck, according to wliich an electrical oscillator absorbs 

 energy from radiation continuously, but emits energy by whole 

 quanta at once. According to the fundamental hypothesis underlying 

 this paper, a similar behaviour should therefore be made also for 

 the ideal gas. 



In order to be able to write down an expression for the total 

 energy of the whole system we need the knowledge of the "spectrum" 

 of the gas. We will suppose, that this spectrum can be determined 

 in a way corresponding to that in w^iich the spectrum of a solid is 

 determined by Debije. 



With these data the equation of state of an ideal monatomic gas 

 can be deduced, and then all thermodynamic quantities for such a 

 gas can be derived. The pressure is found "") to be greater than the 

 "equipartition value" /; = ^^/^ ; at high temperatures it deviates 

 little from this value, the ratio of this deviation to the M\lue itself 

 approaching ultimately indefinitely to 0; at low temperatures, if the 

 gas may then still be treated as an ideal one, the pressure approaches 

 to a value which depends upon the molecular weight and upon 

 the density, but does not depend upon the temperature. That value 

 we call the cero point pressure. 



For a gas like helium at normal density and say 0° C. the devi- 

 ation from the equipartition value appears to be still small. It has, 

 however, already such a value that for instance in determining the 

 VAN DER Waals quantities «,,- and hv., or in the discussion of the 

 virial coefficients, as was done for the second one in Suppl. N°. 25 

 (Sept. '12) and N". 26 (Oct. '12), that deviation has to be taken 

 into account. The zero point pressure for helium at normal density 

 is found to be V, mm. At greater densities deviations from the 

 equipartition laws become more important. 



For the specific heat at constant volume of a gas like helium 

 (supposed to be ideal) at normal density an appreciable deviation 

 from the constant equipartition value is found only at extremely 

 lo w tem peratures '). Ultimately the specific heat also decreases and 



1) A.Einstein and 0. Stern. Ann. d. Phys. (4j 40 (1913), p. 551. Sackur, I.e., 

 assumes the zero point energy also, as is done in this paper, for the molecular 

 translations. 



3) Gf. 0. Sackuk, I.e. 



*) That the speeific heat of monatomic gases deviates from the equipartition 

 value in an appreciable measure only at extremely low temperatures was ah'eady 

 predicted by Nernst and Lindemann, ZS. f. Electrochem. 17 (1911). p. 826, note 1 ; 

 Nernst, Physik. ZS. 13 (1912), p. 1066. [Note added in the translation.] 



