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I can follow that instead of the internal energy $U$, one may choose to define other quantities such as the enthalpy, $H = U + PV$, the Helmholtz Free energy, $F = U - TS$, and the Gibbs free energy, $G = U + PV -TS$ but I have no intuition for why this so.

I have seen some explanations along the lines of the $PV$ term being the energy required to create a system in some environment with constant $P$ and the $TS$ term being the energy contributed from the environment, but this is not very illuminating to me.

Why is the first law insufficient or inadequate so that one needs these definitions?

glS
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user1936752
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  • This sort of thing has been asked here before, and it's covered in virtually every book on statistical mechanics. You should do some more reading and come back with a more specific question. – lemon Sep 05 '16 at 08:03
  • Have you ever considered why it's called a 'free' energy? The internal energy can not all be used for certain process as the effects of entropy may render part of this energy unavailable for meaningful work. By subtracting the effects of entropy from the internal energy we are left with the energy that is 'freely' available for meaningful work. – nluigi Sep 05 '16 at 09:40
  • @lemon Please post the links to the stack where the same question has been asked before.

    I do not have a stat mech textbook but I found that online sources such as http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/helmholtz.html or Wikipedia do not really explain the point sufficiently.

     – user1936752 Sep 05 '16 at 09:47
  • The enthalpy concept has previously been asked about here : http://physics.stackexchange.com/questions/275062/what-is-enthalpy/275068#275068 Schroeder in Intro to thermal physics covers your question pretty well, imo –  Sep 05 '16 at 10:00
  • As with the question CountTo10 linked, it's not clear to me what the question actually is - the meaning of enthalpy is given e.g. on Wikipedia. You say "this is not very illuminating to me", but you don't actually tell us what doesn't satisfy you about it. What about e.g. "enthalpy is the energy needed to create a system and make room for it" is unclear? – ACuriousMind Sep 05 '16 at 10:43
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    Personally, I haven't found the intuitive descriptions of the other potentials to be helpful. (I've found the same in other situations in which the Legendre transformation creates new potentials.) I think of them as objects that have no physical interpretation (although they may have one, I choose to ignore it) that more easily lead to relationships among quantities. I came to this in the study of electric motors where energy and flux can be swapped out for coenergy and current. Current is much easier to measure than flux. Both lead to the same relationships. – garyp Sep 05 '16 at 12:34

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