Question

Prove that specific heat at constant pressure is always greater than specific heat

at constant volume.​

Answer 1

To prove : specific heat at constant pressure is always greater than specific heat at constant volume.

proof : according to first law of thermodynamics,

Q = ∆U + W ........ (1)

where Q is heat , ∆U is internal energy and W is workdone.

you should know,

• heat at constant pressure = Q
• heat at constant volume = ∆U [ internal energy] because at constant volume workdone would be zero.

heat at constant pressure , Q = nCp∆T

heat at constant volume, ∆U = nCv∆T

workdone , W = P∆V = P × nR∆T/P = nR∆T

now from equation (1),

nCp∆T = nCv∆T + nR∆T

⇒Cp = Cv + R

i.e., Cp > Cv

hence it is proved that specific heat at constant pressure is always greater than specific heat at constant volume.

Answer 2

Explanation:

The heat capacity at constant pressure CP is greater than the heat capacity at constant volume CV , because when heat is added at constant pressure, the substance expands and work. QV = CV △T = △U + W = △U because no work is done. Therefore, dU = CV dT and CV = dU dT