Why is Gibbs and Helmholtz free energy defined with the TS term?

[A. Neumaier]

Yes, I read the whole thread, but not all of it pertains to the interpretation of G=H-TS and this is what I emphasized.
I would like to know applications of G outside chemistry: is it used in mechanics ? In electrical systems ? I look for the domain of application, which might help us.
btw: If G=H-TS, then G only applies to systems for which H is defined: which cannot be more often then for systems for which H applies.

G and H are defined for _every_ thermodynamic system; you can go between the two by a standard Legendre transform. depending on the application (and on the tabulated values for your system of interest, you choose one of the two (or another potential, such as that by Helmholtz). All these descriptions are equivalent, but calculating with one description may be far simpler than with another one.

 

[Zeppos10]

G and H are defined for _every_ thermodynamic system; you can go between the two by a standard Legendre transform. depending on the application (and on the tabulated values for your system of interest, you choose one of the two (or another potential, such as that by Helmholtz). All these descriptions are equivalent, but calculating with one description may be far simpler than with another one.

For the discussion on "Why (not) the Legendre Transform" see post #7 at
https://www.physicsforums.com/showthread.php?t=313535

 

[A. Neumaier]

For the discussion on "Why (not) the Legendre Transform" see post #7 at
https://www.physicsforums.com/showthread.php?t=313535

Callen, one of the first to convert to the LT-approach of thermodynamics, writes in 1987 (Thermodynamics etc, p138): "the introduction of the transformed representations is purely a matter of convenience".

True. And in complicated problems, there is a BIG difference between which formulation one uses - in one a particular problem may be tractable, in another one not.

1. First of all: there is nothing convenient about the Legendre transform.

Others find it _very_ convenient; that's why it made it into all textbooks.

2. In general (for an arbitrary, but well defined system), both U(V,S) and H(p,S) are unknown (unspecified) functions:

But in general (for any particular specific system), both U(V,S) and H(p,S) are convex functions, and one of the two (or, more often the Gibbs or Helmholtz free energy) is usually approximately known, and can be used for predictions.

 

[Studiot]

I do believe that equations and conditions involving G are of particular use in multicomponent systems.

As such you will find G used in alloy metallurgy and flow processes such as combustion engines, where the chemical reaction is secondary to the mechanical considerations.

Whether you consider this Chemistry, Chemical Engineering or Mechanical Engineering is moot.