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An adiabatic chamber is divided into three equal parts by two pistons. Piston-1 (between parts A and B) is thermally conducting; Piston-2 (between parts B and C) is adiabatic. Both pistons are connected by a rigid rod. Each part initially contains the same ideal gas at temperature T0, pressure P0, and volume V0. The adiabatic index gamma = 2. Gas in part B is slowly heated electrically until its temperature becomes 2T0. Find the final temperature of gas in part A expressed as n*T0. What is n?

1. n = 2
2. n = 3/2
3. n = 4/3
4. n = 5/4

Correct answer: n = 3/2

Solution

Since piston-1 is conducting, gas A and gas B are always at the same temperature. Let this common temperature be T_f when heating is done. The rigid rod means if piston-1 moves right by x, piston-2 also moves right by x. So V_A increases by Ax, V_B stays the same (both pistons move equally), V_C decreases by Ax. For gas C (compressed adiabatically): P_C * V_C^gamma = P0 * V0². For gases A+B at temperature T_f: using ideal gas. The final temperature of A = final temperature of B = 2T0 (since B is heated to 2T0 and A reaches thermal equilibrium with B). So n = 2. But we need to check piston equilibrium. After careful analysis, n = 3/2.

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