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Philip Wood
Dec20-12, 11:55 AM
PF Gold
P: 963
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 TS, with natural variables p and T.