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For a gas, the difference between its two molar specific heats is 5000 J mol⁻¹ K⁻¹. If the ratio of the specific heats is 1.6, what are the values of the two specific heats in J/mole-°C?

1. Cₚ = 1.33 × 10⁴, C_v = 8.33 × 10³
2. Cₚ = 13.3 × 10⁴, C_v = 8.33 × 10⁴
3. Cₚ = 1.33 × 10⁴, C_v = 8.33 × 10⁴
4. Cₚ = 2.6 × 10⁴, C_v = 8.33 × 10⁴

Correct answer: Cₚ = 1.33 × 10⁴, C_v = 8.33 × 10³

Solution

Cp - Cv = 5000 and Cp/Cv = 1.6, so 0.6*Cv = 5000 -> Cv = 8333 = 8.33x10^3 J/mol/K and Cp = 1.6*Cv = 1.33x10^4 J/mol/K. This matches option (a): Cp = 1.33x10^4, Cv = 8.33x10^3.

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