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In the book "An Introduction to Thermal Physics" by Daniel Schroder, I got the following expressions Helmholtz free energy : F = U - TS and Gibbs Free energy : G = H - TS = U + PV - TS

The author explained the intuition behind Gibbs free energy the following wayenter image description here

I found in different places (Chemistry StackExchange, Wikipedia etc.) that Gibbs free energy is the capacity to do non-expansion work and Helmholtz free energy is the capacity to do both expansion work (pressure-volume work) and non-expansion work. But in the definition of Gibbs free energy there is a pressure-volume term which Helmholtz free energy does not have. Therefore, my intuition is that it should be the other way around. What am I missing here? I would really appreciate if anyone could help me with this.

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  • $\begingroup$ It isn't clear why you think that. $\endgroup$
    – Chet Miller
    Commented Aug 16, 2020 at 11:51
  • $\begingroup$ F = U - TS and G = U + PV - TS. So, G has a pressure-volume term (the + PV term). Therefore, it should include expansion work, I think. $\endgroup$
    – Noob
    Commented Aug 16, 2020 at 12:54
  • $\begingroup$ Are you asking how to derive the equation for the maximum work in terms of G? $\endgroup$
    – Chet Miller
    Commented Aug 16, 2020 at 15:36
  • $\begingroup$ No. I was trying to understand the physical interpretation of these terms. $\endgroup$
    – Noob
    Commented Aug 17, 2020 at 5:48

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But in the definition of Gibbs free energy there is a pressure-volume term which Helmholtz free energy does not have. Therefore, my intuition is that it should be the other way around.

The Gibbs free energy definition $G=U+PV-TS$ doesn't add an expansion term, it removes it. The internal energy $U$ is $U=TS-PV+\Sigma_i \mu N_i$, where $\mu$ is the chemical potential and $N_i$ is the amount of species $i$. Thus, $G=\Sigma_i \mu N_i$, which is why we also call $\mu$ the partial molar Gibbs free energy of species $i$. The process of defining $G$ thus strips away the factors associated with heating and expansion work.

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  • $\begingroup$ Hi! Thank you very much for the answer. It was really helpful. So, Chemical potential energy is the energy stored in the chemical bonds, right? $\endgroup$
    – Noob
    Commented Aug 17, 2020 at 5:54
  • $\begingroup$ Chemical bonds don't store energy; they release it. Bonds form because they sit at a lower energy potential than their constituents, and this energy has to be re-supplied to break them. $\endgroup$
    – Chemomechanics
    Commented Aug 17, 2020 at 17:12

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