Thermodynamics, Statistical Physics, and Quantum Mechanics

134

Here we used the factthat the sumdepends only ontemperature, so we

can define

b) Now we can calculate thetotal entropy of the twogases (it isimportant
that thegases beidentical so that isthe same for bothvessels):

We have fortotalentropy

c) After thevessels areconnectedtheirvolume becomes the
number of particles becomes 2N, and the temperature remains the same
(no work isdone in mixing the two gases). So now

whereFis defined by (S.4.38.4).

SOLUTIONS