B.4.2 (HL)—Gas work

Work from pressure and volume

For a constant-pressure change, the work done by the gas is

$$W=P\Delta V$$

Expansion has $$\Delta V>0$$ and work done by the gas is positive in the first-law convention.

PV interpretation

On a pressure–volume diagram, work is the area under the process path. For constant pressure this is a rectangle; for changing pressure, use the area or integral specified by the model.

Units and direction

Use pressure in pascals and volume in cubic metres so $$P\Delta V$$ is in joules. Compression gives $$\Delta V<0$$, so work done by the gas is negative.

Worked example from the mapped local textbook

A gas expands at constant pressure $1.0\times10^5\,\mathrm{Pa}$ from $0.020\,\mathrm{m^3}$ to $0.050\,\mathrm{m^3}$.

$$W=P\Delta V=(1.0\times10^5)(0.050-0.020)=3.0\times10^3\,\mathrm{J}$$

The work is positive because the gas expands and does work on its surroundings.

Common trap

Do not multiply pressure by the final volume alone. Work depends on the change in volume and on the process path.