- #1

Dario SLC

## Homework Statement

The question is:

What happened with the entropy in a free expansion? The system is isolated and the state equation is:

$$p=AT/V+B/V^2$$

## Homework Equations

$$dU=TdS-pdV$$

## The Attempt at a Solution

My attempt is:

Because the system is isolated and corresponding to an free expansion then the energy is constant since there aren't interchange of heat and work, but there is a work due to expansion of the gas, that is ##pdV##. Then the first and second principle is:

$$TdS-pdV=0$$

then the entropy it can be calculated for integration and using the state equation, and because the initial volume is than minor final volumen, the entropy must increase like must be.

$$S(T)=A\ln\left(\frac{V_2}{V_1}\right)+\frac{B}{T}\left(\frac{V_2-V_1}{V_2V_1}\right)>0$$

My doubt is if this argument valid for any gas or only must be ideal gas? The state equation isn't of the ideal gas, is similar to van der Waals gases.

Thanks a lot!