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## Homework Statement

The question asks whether it is always true that

[tex]dU=C_VdT[/tex]

and their answer is no, because from the 1st law of TD we derive that:

[tex]dU=C_VdT+\left(\frac{dU}{dV}\right)_TdV[/tex]

However, if we hold the volume constant, dV=0 and therefore the second term disappears, is this right?