Adiabatic Work (W = (P₁V₁ - P₂V₂)/(γ - 1))
jee-mainjee-advancedneet-ug
W = (P₁V₁ - P₂V₂)/(γ - 1)
What each symbol means
| Symbol | What it stands for |
|---|---|
| W | Work done by the gas (J) |
| γ | Adiabatic index = Cₚ/Cᵥ (dimensionless, always > 1) |
| P₁ | Initial pressure (Pa or atm, consistent units) |
| P₂ | Final pressure (Pa or atm) |
| V₁ | Initial volume (m³ or L, consistent units) |
| V₂ | Final volume (m³ or L) |
When to use this
Applies to ideal gas undergoing a reversible adiabatic (no heat exchange, Q = 0) process. Also expressible as W = nCᵥ(T₁ − T₂). For expansion P₁V₁ > P₂V₂ so W > 0. For compression P₂V₂ > P₁V₁ so W < 0. γ values: monatomic = 5/3, diatomic = 7/5, polyatomic ≈ 4/3. Adiabatic relation: PVᵞ = constant.