One mole of an ideal gas at 300 K expands isothermally from 1.0 L to 10.0 L. (R = 8.314 J/K-mol = 0.082 L-atm/K-mol; 1 L-atm = 101.3 J; ln 10 = 2.303.) Select the correct statement(s).

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(a) Heat capacity is extensive: false. (b) Δ U = 0 so q rev = w by = nRTln(V 2 /V 1 ) = 8.314 × 300 × 2.303 = 5743 J: true. (c) One-step expansion against 1 atm does w by = 1 × 9 = 9 L-atm = 912 J, so q = 912 J, far less than 5743 J: false. (d) Initial pressure is nRT/V = 0.082 × 300/1 = 24.6 atm. Compression work on the gas = 24.6 × 9 = 221.4 L-atm = 22,430 J. Over the cycle Δ U = 0, so q = -(22,430 - 5743) = -16,690 J, i.e. about 16.7 kJ given out: true. Ans: (b), (d).

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