Arrange the following isothermal processes in order of the magnitude of the work (p - V) involved between states 1 and 2. A. Expansion in single stage w_A B. Expansion in multi stages w_B C. Compression in single stage w_C D. Compression in multi stages w_D Choose the correct option.
C. |w_C| > |w_D| > |w_B| > |w_A|
Let State 1 have pressure P_1 and volume V_1, and State 2 have pressure P_2 and volume V_2. For an isothermal expansion, V_2 > V_1 and P_1 > P_2. For expansion from State 1 to State 2: In a single-stage expansion, the external pressure is constant at the final pressure P_2. The magnitude of work is |w_A| = P_2(V_2 - V_1). In a multi-stage expansion, the external pressure is reduced in steps, keeping it closer to the internal pressure of the gas. The work done by the gas increases with the number of stages, reaching a maximum for a reversible process (|w_ rev |). Thus, |w_ rev | > |w_B| > |w_A|. For compression from State 2 to State 1: In a single-stage compression, the external pressure is constant at the final pressure P_1. The magnitude of work is |w_C| = P_1(V_2 - V_1). In a multi-stage compression, the external pressure is increased in steps. The work done on the gas decreases with the number of stages, reaching a minimum for a reversible process (|w_ rev |). Thus, |w_C| > |w_D| > |w_ rev |. Since P_1 > P_2, the single-stage compression work |w_C| is the largest, and the single-stage expansion work |w_A| is the smallest. The reversible work magnitude |w_ rev | is the same for both expansion and compression between the same states. Combining these inequalities, we get: |w_C| > |w_D| > |w_ rev | > |w_B| > |w_A| Therefore, the correct order of the magnitude of work is |w_C| > |w_D| > |w_B| > |w_A|. Answer: |w_C| > |w_D| > |w_B| > |w_A|
Related: Chemistry — Thermodynamics (C) · All PYQ Banks