One mole of an ideal gas requires 207 J of heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is:
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Question

One mole of an ideal gas requires 207 J of heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is:

Options

G1 Physics · Accepted Answer

Step 1: Heat at constant pressure is Qₚ = nCₚΔT = 207 J. Step 2: With n = 1 mol and ΔT = 10 K, Cₚ = 207/10 = 20.7 J mol⁻¹ K⁻¹. Step 3: Apply Mayer's relation: Cᵥ = Cₚ − R = 20.7 − 8.3 = 12.4 J mol⁻¹ K⁻¹. Step 4: At constant volume: Qᵥ = nCᵥΔT = 1 × 12.4 × 10 = 124 J. Final answer: (D) 124 J.