PdV

pdV refers to the pressure-volume work term in thermodynamics. It represents the infinitesimal amount of work done when the volume of a system changes by an infinitesimal amount dV at pressure p. In a quasi-static, reversible process, the differential work done by the system on its surroundings is δW = p dV, and the total work over a process is W = ∫ p dV.

Sign conventions for pdV can vary. Many physics texts use δW = p dV to denote work done by the system, while some chemistry sources adopt δW = -p dV to denote work done on the system. Because W is path dependent, δ and the sign are important in energy accounting.

Relation to the first law of thermodynamics is given by dU = δQ − δW for a reversible path, so with δW = p dV one has dU = δQ − p dV. This underlies many energy balance calculations for simple compressible systems.

Examples help illustrate pdV. For an isothermal ideal-gas expansion with p = nRT / V, the work is W = ∫ V1^V2 (nRT / V) dV = nRT ln(V2/V1). For a reversible adiabatic process with p V^γ = constant, the work is W = (p2 V2 − p1 V1) / (1 − γ) (or equivalently W = (p1 V1 − p2 V2) / (γ − 1)) depending on sign convention.

In a pressure–volume diagram, the work done during a process equals the area under the p–V curve between the initial and final volumes. The pdV term thus provides a concise way to express the mechanical work exchanged with the surroundings in many thermodynamic problems.