# Math Help - Partial Derivatives with gas, pressure, volume, temperature..

1. ## Partial Derivatives with gas, pressure, volume, temperature..

The gas law for a fixed mass m for an ideal gas at absolute temperature T, pressure P, and volume V is PV = mRT, where R is the gas constant.
Show that бP/бV бV/бT бT/бP = -1

So basically P = mRT/V, V = mRT/P, T = PV/mR are the different functions, and we take the partial derivative of each...but not totally sure how

2. Still looking for this...

3. Take the partial of each by just treating the others as a constant.

$\frac{{\partial}P}{{\partial}V}=\frac{-mRt}{V^{2}}$

$\frac{{\partial}V}{{\partial}T}=\frac{mR}{P}$

$\frac{{\partial}T}{{\partial}P}=\frac{V}{mR}$

Multiply them together:

$(\frac{-mRt}{V^{2}})(\frac{mR}{P})(\frac{V}{mR})=\frac{-mRT}{PV}$

But, $PV=mRT$

Sub it in:

$\frac{-mRT}{mRT}=-1$