# Homework Help: Van der Waals, temperature decrease

1. May 4, 2012

### Gregg

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

I need to find a p-V region where the temperature is decreasing

$(p + \frac{a}{V^2} ) (V-b) = RT$

3. The attempt at a solution

So I thought that a place to start would be

$dT = \frac{\partial T}{\partial P} dP + \frac{\partial T}{\partial V} dV < 0$

So $\frac{\partial T}{\partial P} dP < - \frac{\partial T}{\partial V} dV$

Do I now, $\int \frac{\partial T}{\partial P} dP < - \int \frac{\partial T}{\partial V} dV$?

$\frac{\partial T}{\partial P} = V - b$

$\frac{\partial T}{\partial V} = p + a \log (V) -2 \frac{a b}{V^3}$

Is this the way to do it? The integrals are complicated and I can't really do them