Thermodynamics, Statistical Physics, and Quantum Mechanics

158

Mixtures and Phase Separation

Entropy of Mixing (Michigan, MIT)

a) The energy of the mixture of ideal gases is the sum of energies of the

two gases (since we assume no interaction between them). Therefore the

temperature will not change upon mixing. The pressure also remains un-

changed. The entropy of the mixture is simply the sum of the entropies of

each gas (as if there is no othergas) in the total volume. We may write the

total entropy S (see Problem 4.38) as

SOLUTIONS

where and are the number of molecules of each gas in the mixture.
V is the total volume of the mixture The entropy of the
gases before they are allowed to mix is

Therefore, the change in entropy, is given by

So, (S.4.54.3) becomes

In conventional units we find

The entropy increased as it should because the process is clearly irreversible.

In our case and

4.54

b) If the gases are the same, then the entropy after mixing is given by