1180 
sS—_ = — 
when 4 is the energy of N molecules of gas 
glee de Se et 
u 
When it is borne in mind that pr == kn?’ it follows from (26), 
(27), (28), that: 
: IN E 
S—= — kN logn + — log B — kj Nlogh + 7 + kN, 
u _ 
or when for the sake of simplicity we put n= JN: 
~y 
1 
4 
d yi 
S=klog 6 — kN log N+ kN + pe kj N log hos. Je SO) 
Hence the free energy is: 
FEES TE rr. 31 
eN ae be) > JINN! oh ae eis akte (51) 
We find for the free energy, either by substituting the value (29) 
for E in (30, or by differentiating (81) with respect to 7’: 
S= — era fae — kloq (HIN) — klog(N!),. . ; (32) 
in which: 
e kT if On ds OENE dG 
$ 7. Caleulation of the entropy of gases with arbitrary rigid 
molecules. 
We will now apply the formulae (31), resp. (82) found in the 
preceding § to two simple cases of general oecurrence. 
We can of course first find back the formula (16) of § 3. We 
further find for a gas, the molecules of which possess two rotation 
degrees of freedom with the moment of inertia J, and will be rigid 
for the rest: 
. 
2amkT r QatkT 
Sk {3 Nlog Ep + log N? +. N log —_—— +N log (4) + £ Nj (33) 
Lx . 
2 
2 
which formula we already meet in $$ + and 5. 
For rigid molecules with three rotation degrees of freedom and 
the chief moments of inertia J,, J,, and /,, we find: 
2 
