# Quick Qns : Partial Derivatives

1. Sep 11, 2009

### Legendre

Suppose we are given : PV = nRT, where n and R are constants.

We are told to find the partial derivative dP/dV.

Am I allowed to do this :

P = nRT/V

Then differentiate this w.r.t. to V.

I disregarded the fact that V = 0 makes the RHS undefined.

# This question came from Princeton Review's "Cracking the GRE Math Subject Test" page 160, qns 13.

The solution given uses the above method but I do not understand why V = 0 is not taken into account.

2. Sep 11, 2009

### Hootenanny

Staff Emeritus
When would the volume of an ideal gas ever be zero?

3. Sep 11, 2009

### HallsofIvy

Doing it that way gives
$$\frac{\partial P}{\partial V}= -nRT/V^2$$
You don't need to worry about the fact that V= 0 would make nRT/V undefined because it also makes the -nRT/V2 undefined. That is, the formula you got does not give an answer in exactly the situation where there is no answer.

I would have been inclined to use "implicit" differentiation: from PV= nRT, (dP/dV)V+ P= 0 so dP/dV= -P/V= -(nRT/V)/V= -nRT/V^2.

4. Sep 11, 2009

### Legendre

Thanks a lot guys~ That really helped!