Re: Testing statistical thermo (was: Re: TdS is not dQ or d(anything))

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

Pentcho Valev wrote:

> Here the idea that heat is ESSENTIALLY different from work is clearly
> expressed.
>      Let us test eq. /2/ by considering an analogous situation. We have a large
> group of people each of which possesses a certain amount of money. Let
>
> M = SUM n_i m_i                            /6/
>
> be the total amount of money in the group and n_i is the number of people whose
> money is m_i. Through exchanging money with the outside world M slightly
> changes and the change can be expressed in two ways:
>
> dM = SUM m_i dn_i  +  SUM n_i dm_i                   /7/
>
> dM = SUM m_i dn_i                               /8/
>
> In my view /8/ is correct whereas /7/ is meaningless. If so and if the analogy
> is correct, statistical thermodynamics rests on a wrong foundation. The reason
> is that heat is regarded as essentially different from work.
>
> Pentcho

I'm not sure why you're uncomfortable with the second term in your eqn /7/. Suppose
there is a systematic inflation or devaluation of all the currencies during the
trading process. The dm_i term now makes sense. In a similar fashion, doing work on
the system may change the potentials involved in such a way as to change the
numerical values of the allowed e_i for the n_i particles. Whether or not it's
correct to associate

      sum n_i de_i

with work is a different question, but the term in the equation is not meaningless.

Bob at PC