Where am I going wrong? Thermo derivation..

mcdonkdik

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

Mapes

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