- #1
ultimateguy
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Homework Statement
Use the thermodynamic identity to derive the heat capacity formula [tex]C_V=T\frac{\partial{S}}{\partial{T}}_V[/tex]
Homework 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
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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