Thermodynamics: internal energy and pressure

[LCSphysicist]

Homework Statement

I will post below...

Relevant Equations

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The question is simply why i can't use ∂U/∂V = -P?
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[TSny]

The question is simply why i can't use ∂U/∂V = -P?

When taking partial derivatives, it is important to know what variables are being kept constant.

In order for $P = -\large \frac{\partial U}{\partial V}$ to be true, what variables are to be kept constant?

 

[Chestermiller]

You should be using: $$\left(\frac{\partial U}{\partial V}\right)_T=-P+T\left(\frac{\partial P}{\partial T}\right)_V$$

 

[LCSphysicist]

Yes, when i started thermodynamics i wrongly ignored this terms aside thinking they would be constant anyway as we are dealing with partial derivatives... Now i am doing more advanced i am seeing the importance and the lacune!