FUNDAMENTAL EQUATIONS OF IDEAL GASES 345 



10. \p Function for an Ideal Gas. On substituting its equiva- 



e — Em 

 lent t for • in [255], and solving for rj there results, 



cm 



m 

 r} = mc log t — ma log — + mH, (4) [255] 



07-/-" 



^ = — Q log { — 1 I . . . j e ' dxi dyi dzi, dxi dy\ dzi. (a) 



TTl 



If 6 IS given by ~ (i^ + y* + 2^) there results 



v^ = -elogf-^ j»-t;». (b) 



Applying the operation ——at constant volume and assuming n0 given 



ot 



by at the following analogue of the entropy results : 



17 = I a log i + o log y + I a log ,, . (c) 



Here a definite value of the constant of entropy appears which bears a 

 direct relation to the Nernst Heat Theorem and the so-called chemical 

 constant ^^■^'■^^. Differentiation of equation (b) with respect to the 

 volume at constant temperature and changing the sign gives the fol- 

 lowing expression for the pressure: 



\ovJ V V 



which is equation (II). Again, forming the energy by the operation 



in- 



where t represents kQ~^ — t~^, k being the Boltzmann constant 

 (1.37 X 10-« ergs/deg.) we obtain 



©.-' = 



= -' = I n/c< = I c't. (e) 



Here no constant of energy is assigned nor should a constant appear in 

 view of the properties of a system of structureless mass points treated by 

 classical statistical mechanics. 



