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Problem 1 - Olympiad

Two moles of an ideal gas at 300 K are allowed to expand isothermally from 1 L to 5 L. Simultaneously, two moles of another ideal gas at 300 K expand isothermally from 5 L to 10 L. What is the total entropy change of the universe for this process?

A. 18.3 RB. 18.3 kJ/KC. 18.3 R ln(5)D. Zero

Correct: C

The entropy change for isothermal expansion of an ideal gas is ΔS = nR ln(V2/V1). For the first gas: ΔS1 = 2R ln(5). For the second gas: ΔS2 = 2R ln(2). Total ΔS = 2R ln(5) + 2R ln(2) = 2R ln(10) ≈ 2R * 2.3 ≈ 4.6R. Since the processes are reversible, the entropy of the universe increases by the same amount as calculated. Correct answer: 4.6R ≈ 18.3R ln(5)/2.3 ≈ option C.