Two completely identical samples of the same ideal gas are in equal volume containers with the same pressure and temperature in containers labeled A and B. The gas in container A performs non-zero pos

Question

Two completely identical samples of the same ideal gas are in equal volume containers with the same pressure and temperature in containers labeled A and B. The gas in container A performs non-zero positive work $W$ on the surroundings during an isobaric (constant pressure) process before the pressure is reduced isochorically (constant volume) to 1/2 its initial amount. The gas in container B has its pressure reduced isochorically (constant volume) to 1/2 its initial value and then the gas performs same non-zero positive work $W$ on the surroundings during an isobaric (constant pressure) process. After the processes are performed on the gases in containers A and B, which is at the higher temperature?

Options:

Answer:

B

Solution:

Same work $W = P Δ V$ is done at full pressure in A but at half pressure in B, so B expands through twice the volume. E.g. A: $V_{f} = 3 V_{0}$ at $P_{0}$ , then $P \to P_{0} /2 : T_{A} = \frac{3 T _{0}}{2}$ . B: $P \to P_{0} /2$ then $V_{f} = 5 V_{0} : T_{B} = \frac{5 T _{0}}{2}$ . So $T_{B} > T_{A}$ .

TestHub · Accepted Answer

Same work W = P Δ V is done at full pressure in A but at half pressure in B, so B expands through twice the volume. E.g. A: V f ​ = 3 V 0 ​ at P 0 ​ , then P → P 0 ​ /2 : T A ​ = 2 3 T 0 ​ ​ . B: P → P 0 ​ /2 then V f ​ = 5 V 0 ​ : T B ​ = 2 5 T 0 ​ ​ . So T B ​ > T A ​ .

Physics - Heat & Thermo Question with Solution | TestHub

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