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Carnot Cycle

Two samples A...

Question

Two samples A and B are initially kept in the same state. Sample A is expanded through an adiabatic process and the sample B through an isothermal process. The final volumes of the samples are the same. The final pressures in A and B are p_A and p_B respectively.
(a) p_A > p_B
(b) p_A = p_B
(c) p_A < p_B
(d) The relation between p_A and p_B cannot be deduced.

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Solution

(c) p_A < p_B

Let the initial states of samples A and B be i and the final states of samples B and A be f and f', respectively. Let the final volumes of both be V_o. As sample A is expanded through an adiabatic process, its curve in the p-V diagram is steeper than that of sample B, which is expanded through an isothermal process. Therefore, from the p-V diagram, p_A < p_B.

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