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Work done by a gas

The first law of thermodynamics can be applied to a system of a gas in a container.

The work done by the system (i.e. the gas) can be determined by taking the area under the graph of pressure $$p$$ vs volume $$V$$.

Work done by a gas (represented by the shaded region). The arrow represents the direction of the change (i.e. from an initial to a final state).
Work done by a gas (represented by the shaded region). The arrow represents the direction of the change (i.e. from an initial to a final state).

The work done by the gas is positive when the gas expands and the pressure decreases (the work done on the gas is negative).

The work done by the gas is negative when the gas is compressed and the pressure increases (the work done on the gas is positive).

If the pressure is constant, the work done by the gas can be explicitly calculated by:$$$W=p\Delta V=p(V_{2}-V_{1})$$$$$\Delta V$$ is the change in volume.

Recall from mechanics that $$P=F/A$$ and $$W=Fs$$.