Re: Basic Statistical Mechanics Questions
From: Aaron Denney (wnoise_at_ofb.net)
Date: 01/27/05
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Date: Thu, 27 Jan 2005 21:02:51 +0000 (UTC)
On 2005-01-27, Dan Platt <DanP57@ispwest.com> wrote:
> A standard derivation starts by considering a box with an impermeable
> piston (start with it fixed). Energy is allowed to move by thermal
> conduction from box 1 to box 2 through the piston. Then the
> total change in entropy is
>
> dS = dS1 + dS2 = (dS1/dE1)dE1 + (dS2/dE2)dE2, where dE1 + dE2 = 0.
>
> The (dS1/dE1) are partial derivatives holding V and N const. At this
> point, 1/T = dS1/dE1 is identified. The total entropy change dS >= 0.
> This yields an inequality indicating energy flows from high T to low T
> until T1=T2. Similar arguments can be made for V and N by allowing the
> piston to move and then to become permeable. It is possible to play
> with the derivatives to show that p = T(dS/dV) at const E,N.
More precisely, it indicates a flow from low (1/T) to high (1/T).
In most systems dealt with this is the same, of course, but if
you tweak the thermalization times right, T < 0 is possible
for some well-defined subsystems.
-- Aaron Denney -><-
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