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I'm wondering if there is any difference between Gibbs Free Energy and Exergy because their definition seems to me the same $\Delta H - T_\text{env}\cdot\Delta S$.

Exergy represents the maximum amount of work that can be extracted from a system going in equilibrium with its environment, while the Gibbs Free Energy is evaluated at $T,P$ of the system in equilibrium with the environment.

Practically what is the difference, if any?

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Exergy is equal to the Gibbs free energy if you happen to be in the isothermal--isobaric ensemble $(N, P, T)$, i.e. in a closed system if the pressure $P$ and temperature $T$ are constant. This is indicated in Eq. 7 of the Wikipedia page for exergy.

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    $\begingroup$ I would add a personal note: I've done thermodynamics (and taught it) for many years without ever using the concept of exergy… Although it has some historical relevance, I am not sure how useful it is in a modern presentation of statistical thermodynamics. $\endgroup$ – F'x Aug 11 '16 at 11:35
  • $\begingroup$ Thanks for your precise and clear answer. So Exergy is a way to "call" the free energies depending on the process considered (constant volume-->Helmholtz free energy, constant pressure-->Gibbs free energy)? For example if I considered a stream of hot gas, the maximum work that can be extracted, i.e. its exergy, is the Gibbs free energy if I assume to be at constant pressure? $\endgroup$ – horowitz Aug 11 '16 at 12:46
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Gibbs free energy is calculated without possible PV-work, ie. without volume changes.

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