Thermodynamics of Small Systems, Parts I & II by Terrell L. Hill

Author:Terrell L. Hill
Language: eng
Format: epub
Publisher: INscribe Digital
Published: 2013-04-11T04:00:00+00:00

and so forth.

We start with Eq. (I) and apply to each term the “prime” operation defined in Eq. (158). We use the fact that

and find

By repeating the “prime” operation we also find

These equations are the higher moment analogs of Eq. (I). The coefficients in the first terms are simply related to binomial coefficients.

From Eq. (I(1)) we have

Therefore

and

This is similar to Eq. (III) above. If we use Eq. (I) for S/k, we find

Therefore,

is the next higher analog of Eq. (III).

Similarly, if we start with Eqs. (I(2)), (I(2)), etc., we can derive

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