The molar specific heats of an ideal gas at constant pressure and volume are denoted by Cp and Cv, respectively. If γ = Cp/Cv and R is the universal gas constant, then Cv is equal to

Options

(a) R / ( γ – 1)
(b) (γ – 1) / R
(c) γ R
(d) 1 + γ / 1 – γ

Correct Answer:

R / ( γ – 1)

Explanation:

Cₚ – Cᵥ = R ⇒ Cₚ = Cᵥ + R
γ = Cₚ / Cᵥ = Cᵥ + R / Cᵥ = Cᵥ / Cᵥ + R / Cᵥ
⇒ γ = 1 + R / Cᵥ ⇒ R / Cᵥ = γ – 1
⇒ Cᵥ = R / γ – 1