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4 years, 1 month ago
I was reading through Schroeder's Thermal Physics textbook, where I came across the following (in the section on Helmholtz free energy):
"If the environment is one of constant temperature, the system can extract heat from this environment for free, so all we need to provide, to create the system from nothing, is any additional work needed."
My question is now: Why can a system extract heat for free when the environment is at constant temperature? Or is this the same as saying dW=-dQ for an isothermal process?
Mar 30, 2019 at 15:11
Assume that the surroundings are infinitely large and at temperature
$T_\infty$, and that the system and surroundings are in thermal contact
If the system is at
$T > T_\infty$ then there will be spontaneous heat transfer from the system to the surroundings until the system reaches $T_\infty$
If the system is at
$T < T_\infty$ then there will be spontaneous heat transfer from the surroundings to the system until the system reaches $T_\infty$
This heat energy comes "for free" in that it is given to/taken from the system all by itself. The experimenter doesn't need to give or accept any energy to help the system reach equilibrium.
Note that it's not possible to heat the system above
$T_\infty$ (or cool it below $T_\infty$) "for free." The only change that is "free" is bringing the system to $T_\infty$ and keeping it there.
Apr 3, 2019 at 6:55
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