Register to reply

Derivation of the thermodynamic potentials using Legendre transformations

Share this thread:
Dec20-12, 09:53 AM
P: 3
Hello guys, I'm studying Thermodynamics and I don't totally see how you introduce the potencials using Legendre transformations.

I have seen a non formal explanation showing how you can interpret them, but not a rigorous demonstration of how you get them via the Legendre transformations.

Do you know any site or book that covers it?

Also all the other issues, like the Maxwell transformations and the Euler equations and relations.

Phys.Org News Partner Physics news on
'Squid skin' metamaterials project yields vivid color display
Team finds elusive quantum transformations near absolute zero
Scientists control surface tension to manipulate liquid metals (w/ Video)
Philip Wood
Dec20-12, 11:55 AM
PF Gold
P: 962
I expect I'm not giving you a full picture of what a Legendre transformation is, but here's a systematic way to generate potentials, H, F and G...

Start with dU = TdS- pdV.

From the product rule: dU = TdS- {d(pV) - Vdp}

We can write this as: d{U + pV} = TdS + Vdp

U + pV is usually designated as H. It is the enthalpy potential. Its 'natural variables' are S and P.

We can product-transform TdS instead of pdV, and obtain the Helmholtz function U - TS, with natural variables T and V.

Finally we can transform both TdS and pdV,obtaining the Gibbs function G = U + pV Ė TS, with natural variables p and T.
Dec20-12, 12:10 PM
P: 3
Ok, I see it, is an add and subtract trick, but I don't see where there it's used the Legendre transformation, it's not needed at all?

Dec20-12, 12:14 PM
jtbell's Avatar
P: 11,862
Derivation of the thermodynamic potentials using Legendre transformations
Philip Wood
Dec20-12, 12:48 PM
PF Gold
P: 962
I'd be surprised to be told that I wasn't actually doing Legendre transformations in my earlier post, but let wiser heads decide.

Register to reply

Related Discussions
Thermodynamic potentials Advanced Physics Homework 1
Thermodynamic potentials Classical Physics 0
Thermodynamic potentials and equilibrium Classical Physics 8
Thermodynamic potentials Introductory Physics Homework 1
Help with thermodynamic potentials Classical Physics 10