Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 159

and so In the case of identical gases, reversing the process only

requires the reinsertion of the partition, whereas in the case where two

dissimilar gases are mixed, some additional work has to be done to separate

them again.

c) The same arguments as in (a) apply for a mixture of two isotopes,

and The Gibbs free energy can be written in the form

where and are the chemical potentials of pure isotopes. Therefore,
the potential (S.4.54.7) has the same form as in the mixture of two different
gases, and there is no correction to the result of (a). This is true as long
as (S.4.54.7) can be written in this form, and it holds even after including
quantum corrections to the order of (see, for further details, Landau and
Lifshitz, Statistical Physics, Sect. 94).

4.55 Leaky Balloon (Moscow Phys-Tech)

Let us consider the bag as part of a very large system (the atmosphere)

which initially has N molecules of air, which we consider as one gas, and

molecules of helium. The bag has volume and the number of helium

molecules is Using (S.4.38.7) from Problem 4.38 and omitting all the

temperature-dependent terms, we may write for the initial entropy of the

When the helium has diffused out, we have

We wish to find in the limit where Then

We then obtain

system