pressure-volume work

Pressure-volume work is the mechanical work a gas does when it expands and pushes its surroundings back, or the work done on the gas when something squeezes it smaller. When the gas in a car engine expands, it shoves the piston down, and that push, times the distance the piston travels, is useful work — the same kind of work that turns the wheels. It answers: how much mechanical energy does a changing gas volume deliver or absorb?

When the pressure P is constant, the work done by the gas is simply W = P ΔV, the pressure times the change in volume. This follows directly from work equals force times distance: the gas pushes on a piston of area A with force F = P A, and if the piston moves a distance d the volume changes by ΔV = A d, so W = F d = P A d = P ΔV. When the pressure changes as the gas expands, you add up many thin slices, which in calculus is the integral W = integral of P dV — precisely the area under the path on a PV diagram.

Pressure-volume work is the bridge between heat and motion that makes every heat engine possible. Two honest points about signs: work is positive when the gas expands (it gives energy to the surroundings) and negative when it is compressed (energy comes in). And because the work depends on the whole path taken, not just the start and end states, work — like heat — is not a state function; only internal energy is.