Question

Thermodynamically show that for one mole of an ideal gas Cp - Cv = R.​

Answer 1

By the Equation

ΔQ=ΔU+PΔV

Cv=(ΔQ/ΔT)=(ΔV/ΔT) + P(ΔV/ΔT)

Cp= (ΔQ/ΔT) =(ΔV/ΔT) + P(ΔV/ΔT)

PV=nRT

n=1 (for consideration)

PV=RT

P(ΔV/ΔT)=R

Cp=ΔV/ΔT + R

Cp=Cv + R

Cp - Cv=R