Work in Gas Expansion

Work done by gas in a process: W = ∫P·dV. Always equals the AREA UNDER the curve on a PV diagram.

Sign convention: V increases (expansion) ⇒ W > 0 (gas does work). V decreases (compression) ⇒ W < 0 (work done on gas).

Different processes give different work for same initial-final V — work is a PATH FUNCTION.

Isobaric: W = PΔV (rectangle area).

Isothermal: W = nRT·ln(V_f/V_i) (under hyperbola).

Adiabatic: W = (P_iV_i − P_fV_f)/(γ−1).

Isochoric: W = 0 (ΔV = 0).

Cycle: W_net = enclosed area.