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

Use the thermodynamic identity to derive the heat capacity formula [tex]C_V=T\frac{\partial{S}}{\partial{T}}_V[/tex]

2. Relevant equations

[tex]C_V=\frac{\partial{U}}{\partial{T}}[/tex]

[tex] T=\frac{\partial{U}}{\partial{S}}[/tex]

dU=TdS-PdV+[tex]\mu[/tex]dN

3. The attempt at a solution

I used [tex]C_V=\frac{\partial{U}}{\partial{S}}\frac{\partial{S}}{\partial{T}}=T\frac{\partial{S}}{\partial{T}}_V=\frac{\partial{U}}{\partial{T}}=C_V[/tex].

This is the only solution I can think of, but I don't think I used the thermodynamics identity, did I?

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# Deriving heat capacity using thermodynamics identity

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