Question

derive relation cp and cv

Answer 1

CP. ...specific heat at constant pressure..
CV. .....specific heat at constant volume....
Hope it helps u☺

Answer 2

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 qV = n CV∆T

This value is equal to the change internal energy, that is, qV = 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,

C_P ∆T = C_V ∆T + R ∆T

Or,

Or,       $C_P = C_V + R \\\\C_P - C_V= R$