Hi all, I have a small question about a proof.(adsbygoogle = window.adsbygoogle || []).push({});

Question:

Under control variables T, V, and N, derive an expression to relate internal energy as a function of volume. Assume that N is constant throughout.

Thoughts:

Starting with dU = TdS - PdV + udN.

Cancel out dN --> dU = TdS - PdV

Divide by dV --> (dU/dV) = (TdS/dV) - P

In my answer key,

It jumps from the above equation to (dU/dV) = (TdP/dT) - P

I don't understand why dS/dV was replaced by dP/dT, how was that relationship derived?

Thanks.

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# Thermodynamics Proof

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