# Math Help - gas equation differenciate

1. ## gas equation differenciate

I have no idea to how I should proceed . Here is the question:

Dieterici's equation of state for gas is

$P(V-b)e^{\frac{a}{RVT}} = RT$

Where a, b, and R are constants. Regard volume V as a function of temperature T and pressure P and prove that

$\frac{\partial{V}}{\partial{T}} = \frac{(R+\frac{a}{TV})}{(\frac{RT}{V-b} - \frac{a}{V^2})}$

2. Hi

$V-b=\frac{RT\exp\left(-\frac{a}{RVT}\right)}{P}$

Take the log (it'll be easier to differentiate) : $\ln(V-b)=\ln R +\ln T -\frac{a}{RVT} -\ln P +b$

And then differentiate with respect to $T$. Good luck