A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

where is the concentrationratio of heliummolecules
in the bag to their concentration in the air. In regular units

160 SOLUTIONS

Osmotic Pressure (MIT)

a) The free energy for a one-component ideal gas is derived in Problem

The Gibbs free energy

But so (S.4.56.2) must be transformed:

If we have a mixture of two types of molecules with and particles
each, we find for the thermodynamic potential of the mixture:

4.38:

Substituting the standard pressure and temperature into (S.4.55.5)gives

The minimum work necessary to separate the helium at constant temper-

ature is (see Landau and Lifshitz, Statistical Physics, Sect. 20)

since after we separate the helium moleculesfrom the rest of

the air, the total entropy of that system would decrease. So

4.56