Question

If CP and Cv denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then relation between Cv and Cp is?

Answer 1

ΔQ=ΔU+PΔV
at constant volume ΔV=0
so, ΔQ=ΔU
Cv=ΔQ/ΔT =ΔU/ΔT
Cp=ΔQp/ΔT

    =ΔU/ΔT+PΔV/ΔT
but ΔU/ΔT=Cv
Cp=Cv+PΔV/ΔT
but,PΔV/ΔT=nR
Cp=Cv+nR
n is number of moles
for 1 no of moles
Cp-Cv=R

Answer 2

For one mole :

Cp-Cv=R

For unit mass :

Cp-Cv=R÷molar mass

Thus, for nitrogen gas Cp-Cv=R÷28

(Molar mass of nitrogen gas is 14×2=28)