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The molar specific heats of an ideal gas at constant pressure and volume are denoted

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

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