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Mapes
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Jan10-11, 08:11 PM
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Quote Quote by jeebs View Post
Well, where has the energy available to do work gone due to the disorder?
It has disappeared. There's no Law of Conservation of "Energy Available to Do Work"; there's only the Law of Conservation of Energy, and the energy in your system is unchanged. The entropy has increased, though.

Quote Quote by jeebs View Post
Also, going back to the Helmholtz free energy, it's written as F = U - TS, where U is the internal energy (ie. the potential energy due to the Coulomb interactions of the particles, right) and TS is the entropic term. I always wondered about the TS term, why does it have that form?
We know that closed adiabatic systems at constant volume tend to evolve toward their lowest energy state (i.e., [itex]dU=0[/itex] at equilibrium, where [itex]dU=T\,dS-P\,dV[/itex]). But we often deal with systems at constant temperature rather than adiabatic systems. Therefore, we perform a so-called Legendre transform by writing [itex]F=U-TS[/itex]; this produces [itex]dF=-S\,dT-P\,dV[/itex], which tells us that constant-temperature systems at constant volume tend to minimize [itex]F[/itex] and satisfy [itex]dF=0[/itex] at equilibrium. So that's the quick story of where the [itex]TS[/itex] comes from. Does this make sense?