?34 



h { 9 ]SI\h /5 NkT\k 



^^■'■»"=k{T.v) ■ U^j ■ • • • *^^") 



Taking iV= 6,85. 10", - = 4,86. 10-1', /l-^r 1,21 . 10-16, ^g obtain 



<9r7»ö) =: 45,1 . i¥-V. F-'/3 TV. (15/>) 



^{T»Oj is connected with ó^^ to be introduced in c by the relation 



:i-2 



^(T»0)=::(^--^„TJ • (15.) 



For helium at 0° C. and 1 atra. we find — 13.2. From (14) 

 follows a deviation from Boyj-e's law to an amount of 0.127oo- 

 Tiiis deviation is in the direction found by experiment and has such 

 an amount that with reasonable suppositions about tlie van der Waals 

 constants it is not in conflict with the value experimentally observed ') : 

 0.512Voo- On the other hand there would have been contradiction 

 if in the expression (2) for the energy the zero point energy had 

 not been taken up. This, and a similar result concerning the pressure 

 coefficient of helium between 0° and 100° C. were the reasons 

 which led Prof. Kamkrlingh Onnes and me in our communication 

 to the Woi FSKEHL-congress to the hypothesis of the zero point energy 

 for an ideal gas. 



Although the deviation from Boyle's law, which follows from the 

 application of the quantum-theory in the way explained in this paper, 

 is still small in the special case discussed above, it nevertheless 

 appears (and for greater densities this is even more the case), that 

 in discussing the equation of state this deviation has to be taken 

 into account. Further discussion in this direction has to be postponed, 

 however, to a later communication. 



c. Loiü temperatures. ¥oy low temperatures the following develop- 

 ment ^) is more a})propriate : 



U^- Nk t\~x-\-~-^~ X 2 e--^ _-|- + +,(16) 



2 (8 \h x^ „r=i V^*"^' ^ ''^ *^^ n\x^J\ 



with X acc(n-ding to (11) and (10). The first two terms give (ÏX< <9): 



U— ^NkSAl -\ , (17) 



where 



/r / 9 i\^Y/3 5 Nk 

 8 z= - A . (18a) 



or (cf. b) 



d, = lQ\ .M-^V-'lz (186) 



1) H. Kamerlingh Onnes, Gomm. No. 102a, Dec. 1907. 



2) According to Debye, I.e., suitable from x=z<x: to x = 2. 



