dW

dW denotes an infinitesimal amount of work transferred into or out of a thermodynamic system during a small change of its configuration. In thermodynamics, work is a path-dependent quantity rather than a state function, so dW is typically written with a differential symbol (often δW) to emphasize its inexact differential nature.

For a quasi-static, reversible process on a simple compressible system, the infinitesimal work is dW = p_ext dV, where p_ext is the external pressure and dV is the differential change in volume; for a general force F along a displacement dr, dW = F · dr. In a single-flow gas, dW = p dV where p is the internal pressure; the integral W = ∫ p dV gives the work done by the system during a finite volume change.

Sign conventions vary: in physics, the first law is written dU = δQ − δW, with δW the work performed by the system on its surroundings; in chemistry, W is often defined as work done on the system, in which case the sign is reversed. The key point is that because work depends on the path taken between states, dW is not in general the differential of a state function and cannot be written as a function solely of the system's state.

Because of its path dependence, dW plays a central role in analyses of engines and refrigerators, phase transitions under pressure, and various irreversible processes. It is related to heat transfer by the first law: ΔU = Q − W (sign conventions vary).