An ideal gas in a cylinder is compressed in a **single step** from volume Vᵢ to volume Vf (Vf < Vᵢ) by a constant external pressure pₑₓ. The shaded area in the figure represents the work done on the gas. Which expression correctly gives this work? 

Force × distance gives $w = p_{ex} \cdot A \cdot l$, and the sign convention (work done on the gas is positive) requires $w = -p_{ex}\Delta V = -p_{ex}(V_f - V_i)$. Since Vf < Vᵢ here, (Vf − Vᵢ) is negative and the work comes out positive — consistent with the system gaining energy during compression. (B) flips the sign (gives negative work for compression — wrong). (C) is the **reversible** isothermal expression, not single-step. (D) holds only for free expansion into vacuum (pₑₓ = 0).