(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that if a single-component system is such that PV^{k}is constant in an adiabatic process (k is a positive constant) the energy is U = [1/(k-1)]PV + Nf(PV^{k}/N^{k}) where f is an arbitrary function.

2. Relevant equations

Fundamental relation: U = [1/(k-1)]PV + Nf(PV^{k}/N^{k}).

State equations: T = δU/δS, P = - δU/δV, μ = δU/δN.

3. The attempt at a solution

PV^{k}has to be a function of S, so that (δU/δV)S = g(S) x V^{-k}, where g(S) is an unspecified function, and V^{-k}is V^{k}inverse.

I think I'm going to end up finding dU first, and integrating to find U, but pretty much, I'm stuck here. Any help at all would be greatly appreciated.

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# Homework Help: Please Help Quickly Thermo Single-Component Adiabatic System Derive Energy Equation

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