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Helmholtz Free Energy Legendre Transformation

  1. May 13, 2015 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant 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

    3. 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
     
  2. jcsd
  3. May 18, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. May 19, 2015 #3

    rude man

    User Avatar
    Homework Helper
    Gold Member

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