Q.29

Which of the following conditions is CORRECT for free expansion of an ideal gas under

adiabatic condition? (q = heat, ΔT = temperature difference, w = work)

(A) q = 0, ΔT < 0, w ≠ 0

(B) q = 0, ΔT ≠ 0, w = 0

(C) q ≠ 0, ΔT = 0, w = 0

(D) q = 0, ΔT = 0, w = 0

Free Expansion of Ideal Gas Under Adiabatic Conditions: Correct Answer Explained

Free expansion of an ideal gas under adiabatic conditions occurs when the gas expands into a vacuum with no heat exchange. The correct option is (D) q = 0, ΔT = 0, w = 0, as confirmed by the first law of thermodynamics where ΔU = q + w = 0 leads to no temperature change for ideal gases.

Key Thermodynamics Principles

In adiabatic processes, no heat transfer happens, so q = 0 by definition. Free expansion means the gas expands against zero external pressure, making work done w = -P_ext ΔV = 0. For ideal gases, internal energy U depends only on temperature, so ΔU = nC_v ΔT = 0 implies ΔT = 0.

Option-by-Option Analysis

• (A) q = 0, ΔT < 0, w ≠ 0: Incorrect. While q = 0 holds, free expansion has w = 0, and ΔT remains zero, not negative, unlike reversible adiabatic expansion.

• (B) q = 0, ΔT ≠ 0, w = 0: Incorrect. q = 0 and w = 0 are right, but ΔT must be exactly 0 for ideal gases since ΔU = 0.

• (C) q ≠ 0, ΔT = 0, w = 0: Incorrect. Adiabatic conditions require q = 0; non-zero q violates the no-heat-transfer rule.

• (D) q = 0, ΔT = 0, w = 0: Correct. All parameters align: no heat, no work, no temperature change in free adiabatic expansion of ideal gas.

Why This Matters for Exams

This concept tests understanding of the first law (ΔU = q + w) and ideal gas properties, common in NEET and JEE questions on thermodynamics.