Thermodynamics

Question 1

Derive the relationship between heat capacity at constant pressure (Cp) and heat capacity at constant volume (Cv) for an ideal gas.

Answer 1

At constant volume: q(v) = C(v) ∆T = ∆U (I)
At constant pressure: q(p) = C(p) ∆T = ∆H (II)

For mole of an ideal gas: ∆H = ∆U + p∆V
∆H = ∆U + ∆(pV)
∆H = ∆U + ∆(RT)
∆H = ∆U + R∆T (III)

From (I) and (II) into (III):
Cp∆T = Cv∆T + R∆T
Cp = Cv + R
Therefore, relationship:
Cp - Cv = R