Work Done On and By a Gas

Picture gas molecules in a cylinder, drumming on a piston. If the piston is free to move and the gas pushes it outward, the molecules are shoving a wall, and anything that shoves a wall and moves it is doing work. That work has to come from somewhere, and the only energy the gas has to spend is its own internal energy, the kinetic energy of its bouncing molecules. Spend that energy pushing the piston and the molecules slow down. Slower molecules means a colder gas. No heat left the system by flowing through a wall as heat, it left as mechanical work, and the gas cools because it paid for its own expansion.

At constant pressure this trades energy for distance in a clean way: work equals pressure times the change in volume, W = PxDeltaV. Squeeze the gas and its volume drops, so work is done ON it, adding energy; let it expand and it does work ON its surroundings, spending energy. The sign is just bookkeeping for which direction the energy moves.

This sets up the first law of thermodynamics, DeltaU = Q minus W, where this work term sits right next to heat as the second way energy can enter or leave a gas. When pressure holds steady, the work is that simple rectangle P times DeltaV; when pressure changes during the process, the work is the area under the curve on a pressure-volume graph instead, since P is no longer a constant you can just multiply through. Either way, the gas rushing into a vacuum is the limiting case that shows work needs something to push against.