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## Main Question or Discussion Point

Cv = (∂U/∂T)v = T(∂S/∂T)v

I can prove this by using the Maxwell relations, but I have trouble deriving it from the first law.

dU = TdS - pdV

(∂U/∂T)v = T(∂S/∂T)v + ∂S(∂T/∂T)v = T(∂S/∂T)v + ∂S

Is there a problem with my derivation?

I can prove this by using the Maxwell relations, but I have trouble deriving it from the first law.

dU = TdS - pdV

(∂U/∂T)v = T(∂S/∂T)v + ∂S(∂T/∂T)v = T(∂S/∂T)v + ∂S

Is there a problem with my derivation?