The volume V of a monoatomic gas varies with its temperature T as shown in the graph (a straight line through the origin, V ∝ T). The ratio of work done by the gas to the heat absorbed when it goes from state A to state B is:
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Question

The volume V of a monoatomic gas varies with its temperature T as shown in the graph (a straight line through the origin, V ∝ T). The ratio of work done by the gas to the heat absorbed when it goes from state A to state B is:

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G1 Physics · Accepted Answer

Step 1: For an ideal gas, PV = nRT. If V ∝ T, then P = nRT/V is constant; the process is isobaric. Step 2: Work done in isobaric heating: W = PΔV = nRΔT. Step 3: For a monoatomic ideal gas, Cₚ = (5/2)R per mole. Step 4: Heat absorbed: Q = nCₚΔT = (5/2)nRΔT. Step 5: W/Q = (nRΔT)/[(5/2)nRΔT] = 2/5. Final answer: (A) 2/5.