Helmholtz Free Energy Legendre Transformation

[says]

Homework Statement

Show how a Legendre transformation is used to obtain the Helmholtz free energy A(T,V) from the internal energy and derive the general expression for the differential of A.

Homework Equations

Internal Energy is a function of Entropy and Volume.

U Ξ (S, V)

A Ξ (T,V)

A = U - TS

where
U: Internal Energy
S: Entropy
V: Volume
T: Temperature
A: Helmholtz Free Energy

The Attempt at a Solution

A = U - (dU/dS)_VS

dU = TdS - pdV

(dU/dS)_V = T

A = U - TS (Helmholtz free energy)

dA - dU - TdS-SdT

dA = TdS - pdV - TdS - SdT

dA = -SdT - pdV

A Ξ (T,V)

I just wanted someone to check my derivation as I'm still a bit new to Legendre transformations. Cheers

 

[rude man]

I would post this in the advanced physics forum. It's not introductory material.