Work done by gas and how engines work

Heat gas in two vessels: one has a fixed lid, while the other has a piston that can rise. Gas exerts pressure in both. Why does it do mechanical work on its boundary only in the second?

Gas particles strike the walls and produce pressure. A force acts on a piston, but force alone is not enough for work: recall a stationary load on a table. If the piston moves outwards under the gas force, the gas does positive work and transfers mechanical energy. Work A is measured in joules. Work on a fixed lid is zero, even if the pressure is very high.

Expansion alone does not produce work. When gas moves a piston against external forces, the energy comes either from heat supplied or from the gas's own internal energy. Without heat input, such gas usually cools as its internal energy decreases. Compare this with expansion into an empty part of a rigid vessel. There is no movable external object receiving energy, so an increase in volume alone does not guarantee work.

Now push the piston to compress the gas. The external force moves the boundary against the pressure force, so work is done on the gas. This energy can raise its internal energy and temperature, as when air is compressed quickly in a pump. If the gas has time to transfer energy out, the temperature rise is smaller. Boundary motion determines the direction of energy transfer by work, while temperature change also depends on heat exchange.

One expansion gives only one piston stroke. For continuous operation, an engine must return its mechanism to a position from which the process can repeat. In a piston internal combustion engine, fuel burns inside the cylinder and gas transfers energy to the mechanism. The used gas cannot expand indefinitely: combustion products must be removed and a fresh charge prepared. This produces a repeating sequence of processes, a cycle.

Consider a simple four-stroke petrol engine. During intake, the piston opens up volume and the mixture enters through an open valve. The valves then close and the piston compresses the mixture. During this stroke, work is done on the gas; it does not supply work. The rotating mechanism connected to the piston drives the motion: stored energy and work from other cylinders carry it through strokes in which this cylinder does not accelerate the shaft.

After ignition, the gas temperature and pressure rise rapidly. The gas expands and pushes the piston: this is the power stroke, which transfers energy to the shaft. The exhaust valve then opens and the piston expels the used gases. Only after exhaust is there space for the next intake. Assess the useful output over the whole cycle: some work gained during the power stroke is used for compression, gas exchange and overcoming friction.

Must gas push a piston? Direct a steam flow onto blades instead: as they change the flow's motion, a force acts on them and the shaft rotates. This is how a steam turbine works. Steam is produced outside the turbine and supplied to it; its energy becomes mechanical energy of rotation. The shaft can drive an electric generator. Turbine and generator perform different stages: first rotation is produced, then electrical energy.

In one cylinder, heated gas is trapped by a rigid, fixed lid; in another, it lifts a piston. Where does the gas do mechanical work on the lid or piston?

First check for force: gas pressure acts on both the fixed lid and the movable piston.

Then check displacement of the point where the force acts. The lid is stationary, so the gas does zero work on it. The piston rises and receives mechanical energy from the gas.

The difference is whether the boundary can move, not merely whether heating occurs: in a fixed vessel, the supplied energy can increase the gas's internal energy.

Work on the lid or piston is done in the second cylinder. In the first, pressure exists but the lid does not move.

Pressure does mechanical work when it moves a boundary against external forces.

Expansion with work transfers energy out; compression transfers energy to the gas. Heat exchange can change the resulting temperature rise.

Four strokes make repeated operation possible; in a turbine, the flow acts on blades instead of a piston.

A heat engine converts only part of the energy it receives into work. Next, we will calculate this fraction.