# Adiabatic expansion of a monatomic gas

1. Sep 9, 2007

### anchovie

1. The problem statement, all variables and given/known data

The molar energy of a monatomic gas which obeys van der Waals' equation is given by

E = (3/2)RT - a/V

V volume, T temperature, a is a constant. Initially you have T1 at V1, and the gas expands adiabatically in a vacuum so that you have V2. What is T2?

2. Relevant equations

Van der Waals' equation: P = RT/(V - b) - a/V^2

3. The attempt at a solution

Q = 0, so dW = dE. dW = -PdV, and I rewrite P in terms of V and T according to van der Waals' equation, then try to rearrange terms so that I can integrate, but I don't think the terms are separable, and I'm beginning to wonder if there is something wrong in my approach. Any help would be appreciated.

2. Sep 9, 2007

### Gokul43201

Staff Emeritus
You have $dE = (3R/2)dT + (a/V^2)dV$ and you can also write an expression for RdT from the VdW equation. Plug in for RdT from the second into the first, and set dE + PdV = 0. This should leave you with a DE in (P,V). What does it look like? Is this the equation you say is not separable?