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
Still looking for this...:(
Take the partial of each by just treating the others as a constant.
$\displaystyle \frac{{\partial}P}{{\partial}V}=\frac{-mRt}{V^{2}}$
$\displaystyle \frac{{\partial}V}{{\partial}T}=\frac{mR}{P}$
$\displaystyle \frac{{\partial}T}{{\partial}P}=\frac{V}{mR}$
Multiply them together:
$\displaystyle (\frac{-mRt}{V^{2}})(\frac{mR}{P})(\frac{V}{mR})=\frac{-mRT}{PV}$
But, $\displaystyle PV=mRT$
Sub it in:
$\displaystyle \frac{-mRT}{mRT}=-1$
