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Derive a relation between cp and cv |
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Answer» 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 |
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