Thermodynamics: internal energy and pressure

LCSphysicist · Aug 18, 2020

Printed text reading 'The state equation of a new matter is' followed by the equation p = AT³/V, where p is pressure, A is a constant, T is temperature and V is volume.

Printed problem text: where p, V and T are pressure, volume and temperature, A is a constant. Internal energy U = BT^n ln(V/V0) + f(T), where B, n and V0 are constants and f(T) depends only on temperature. Find B and n. (CUSPEA)

The question is simply why i can't use ∂U/∂V = -P?
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TSny · Aug 18, 2020

LCSphysicist said:

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 · Aug 18, 2020

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

LCSphysicist · Aug 19, 2020

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!

Thermodynamics: internal energy and pressure

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