An ideal gas undergoes isothermal expansion from (10 atm, 1 L) to (1 atm, 10 L) either by path-I (infinite stage expansion) or by path-II (first against 5 atm and then against 1 atm). The value of (q_

Question

An ideal gas undergoes isothermal expansion from (10 atm, 1 L) to (1 atm, 10 L) either by path-I (infinite stage expansion) or by path-II (first against 5 atm and then against 1 atm). The value of (q_path-I / q_path-II) is

Prashant Kotian · Accepted Answer

Correct answer: A. Path-I is reversible: q1 = -w1 = nRT ln(V2/V1) = P1 V1 ln(10) = 10 * 1 * 2.303 = 23.03 L-atm. Path-II is two-stage irreversible: Intermediate volume at P=5 atm is V' = 10/5 = 2 L. w_stage1 = -5 * (2 - 1) = -5 L-atm. w_stage2 = -1 * (10 - 2) = -8 L-atm. Total work w2 = -13 L-atm => q2 = +13 L-atm. Thus, ratio q1/q2 = 23.03 / 13 = 2.303 / 1.3.

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