Relationship between CP and CV for an Ideal Gas
From the equation q = n C ∆T, we can say:
At constant pressure P, we have qP = n CP∆T
This value is equal to the change in enthalpy, that is, qP = n CP∆T = ∆H
Similarly, at constant volume V, we have q
V = n CV∆T
This value is equal to the change internal energy, that is, q
V = n CV∆T= ∆U
We know that for one mole (n=1) of ideal gas,
∆H = ∆U + ∆(pV )
= ∆U + ∆(RT )
= ∆U + R∆T
Therefore, ∆H = ∆U + R ∆T
Substituting the values of ∆H and ∆U from above in the former equation,
CP∆T = CV∆T + R ∆T
Or CP = CV + R
Or CP – CV= R
