Moving Walls and Maximizing Microstates: It's Obvious. Not!

This installment of “It’s Obvious. Not!” looks at:

Book: “Statistical Mechanics”

Edition: second

Authors: R.K. Pathria

Publisher: Elsevier Butterworth Heinemann

Page: 14

Section 1.3 follows the derivation laid out in 1.2, but with a variable volume to arrive at:

As in 1.2, a parameter is defined that must be equalized:

The above subscript notation indicates that N and E are held constant and that V is equal to its equilibrium value.

The basic formula of thermodynamics is then stated as:

Immediately after which, it is stated that:

But how?

First, remembering that N and E are constant, rewrite the basic formula above as:

Now, using the expression from section 1.2 relating the micro and macro states:

We can write:

However,

so,

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