Question

The gas law for a fixed mass m of an ideal gas at absolute temperature T, pressure P, and volume V is PV=mRT, where R is the gas constant. Find the partial derivatives

Answer 1

Answer:

the equation is

P*V = mRT.

The partial derivatives are:

For P = mRT/V.

$dP/dV = -\frac{mRT}{V^2}$

$dP/dT = \frac{mR}{V}$

now, if we take:

V = mRT/P

$dV/dT = \frac{mR}{P}$

$dV/dP = -\frac{mRT}{P^2} = (dP/dV)^{-1} = -\frac{V^2}{mRT}$

If we take T = PV/mR

$dT/dP = \frac{V}{mR} = (dP/dT)^{-1}$

$dT/dV = \frac{P}{mR} = (dV/dT)^{-1}$