Work in Gas Expansion
W = ∫P dV — area under PV curve, 3 paths.
Key Notes
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.
Formulas
General work
Area under PV curve.
Isobaric
Constant pressure.
Isothermal (ideal gas)
Logarithmic.
Adiabatic (ideal gas)
γ = C_p/C_v.
Isochoric
No volume change ⇒ no work.
Important Points
Work is a PATH FUNCTION — depends on HOW the process proceeds, not just endpoints.
Different processes between same initial and final states give different W values.
Area under PV curve = work. Positive for expansion, negative for compression.
Isochoric: W = 0 (vertical line — no horizontal sweep).
Isobaric: W = PΔV (rectangle).
Cycles: net W = enclosed area; clockwise positive, counter-clockwise negative.
Work in Gas Expansion notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.