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Where am I going wrong? Thermo derivation

  1. Oct 13, 2011 #1
    Derive the fundamental equations of thermodynamics for an open system containing a onecomponent fluid in terms of the intensive internal energy U = U/N, the intensive Helmholtz free energy A, the intensive Gibbs free energy G, and the intensive enthalpy H. For each of the equations write the one associated Maxwell relation. Hint: The starting point should be
    U = −pV + TS + μ. U = (U/N) etc..

    Right, so I can do it in therms of U, however I'm stuck on A and some others.. my working below:

    For A:

    A=-ST - pV + μ

    dA = d(A/N) = (1/N)dA + Ad(1/N)

    = (1/N)(-SdT - pdV + μdN) + d(1/N)(-ST - pV + μ)

    Recognising that: dV(underlined) = NdV + NVd(1/N) .. I'm guessing I need to eliminate dV? I'm not sure why though... :S

    dA = (1/N)[-SdT - p(NdV + nVd(1/N)) + μdN] + [-STd(1/N) - pVd(1/N) + μd(1/N)]

    = -SdT - pdV + (μ/N)dN + μd(1/N) - STd(1/N)

    I can't get the last 3 terms in bold to disappear.. help! Anyone know what I'm doing wrong?

    Its meant to go down to dA = -SdT - pdV


    Many thanks
     
    Last edited: Oct 13, 2011
  2. jcsd
  3. Oct 13, 2011 #2

    Mapes

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    Your definition of A is off: A=U-TS.
     
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