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

216 SOLUTIONS

where weused Substituting and from

(S.4.93.21), we obtain a more general formula for

At constant volume (S.4.93.23) becomes

the same as before.

4.94 Number Fluctuations (Colorado (a,b), Moscow

Phys-Tech (c))

a) Using the formula derived in Problem 4.92, we have

Consider an assortment of particles which are in the quantum state.
They are statisticallyindependent of theother particles in thegas;therefore
we can apply (S.4.94.1) in the form

For a Fermi gas

So, by (S.4.94.2),