Question

What is the partial derivative of pressure with respect to volume for an ideal gas?

use PV=nRT

Answer 1

in an ideal gas equation PV = nRT

              V = f(P,T,n); that is, V = nRT/P

differentiate with respect to temperature we get

(∂V/∂T)_n,P = nR/P       

differentiate with respect to pressure

(∂V/∂P)_n,T = nRT/P²        

differentiate with respect to number of moles

(∂V/∂n)_P,T = RT/P

P = nRT/V

differentiate with respect to temperature we get

(∂P/∂T)_n,P = nR/V       

differentiate with respect to volume

(∂P/∂V)_n,T = nRT/V²        

differentiate with respect to number of moles

(∂P/∂n)_P,T = RT/V