Match the LIST-I with LIST-II $\begin{array}{|l|l|c|l|} \hline \text{List-I} & \text{Isothermal process} \\…

Match the LIST-I with LIST-II $\begin{array}{|l|l|c|l|} \hline \text{List-I} & \text{Isothermal process} \\ & \text{for ideal gas system} & \text{List-II} & \text{Work done } (V_f > V_i) \\ \hline \text{A.} & \text{Reversible expansion} & \text{I.} & w = 0 \\ \hline \text{B.} & \text{Free expansion} & \text{II.} & w = -nRT \ln \frac{V_f}{V_i} \\ \hline \text{C.} & \text{Irreversible expansion} & \text{III.} & w = -p_{\text{ex}}(V_f - V_i) \\ \hline \text{D.} & \text{Irreversible compression} & \text{IV.} & w = -p_{\text{ex}}(V_i - V_f) \\ \hline \end{array}$ Choose the correct answer from the options given below:
  1. A-I, B-III, C-II, D-IV
  2. A-II, B-I, C-III, D-IV
  3. A-IV, B-I, C-III, D-II
  4. A-IV, B-II, C-III, D-I

Solution

Matching isothermal processes with work expressions:
A. Reversible expansion: In a reversible isothermal expansion from $V_i$ to $V_f$ (where $V_f > V_i$), the gas does work against external pressure equal to the surroundings. The work is $w = nRT \ln \frac{V_f}{V_i}$, matching II.
B. Free expansion: The gas expands into a vacuum with no external pressure opposition. No work is done: $w = 0$, matching I.
C. Irreversible expansion: Isothermal expansion from $V_i$ to $V_f$ against constant external pressure $p_{ex}$. Work done is $w = -p_{ex}(V_f - V_i)$, matching III.
D. Irreversible compression: Isothermal compression from $V_i$ to $V_f$ (where $V_f < V_i$) against constant external pressure. Work is $w = -p_{ex}(V_i - V_f)$, matching IV.

The correct pairings are A-II, B-I, C-III, D-IV.

Asked in: JEE Main 2026 (24 Jan Shift 1)

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