Thermodynamics, Statistical Physics, and Quantum Mechanics

129

The condition alsoimpliesthat Then we may approximate

So,(S.4.35.3) becomes

where weused the averagenumber ofmolecules inV:

Noticingthat, forlarge.

we obtain

where we used

(S.4.35.6) canbe applied tofind the mean square fluctuation in anideal gas

(seeProblem 4.94) when the fluctuations are notnecessarilysmall(i.e., it is

possible to have althoughNis always much smaller

than the total number of particles in the gas

THERMODYNAMICS AND STATISTICAL PHYSICS