The ideal gas law is PV nRT where P is the pressre V is the

The ideal gas law is PV = nRT, where P is the pressre, V is the volume. T is the absolute temperature, n is the number of moles of gas, and R is a constant. Show that:

Solution

dV/dT = nR/P

dT/dP = V/nR

PV = nRT

P dV + VdP = 0

dP/dV = - P/V

Multiplying we get

dP/dV * dV/dT * dT/dP = -P/V * ( nR/P) * ( V/nR)

= -1