Match the List-I with List-II ( List-I Isothermal process for ideal...

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.