16.2 Work Done by a Gas

Work Done by a Gas

• When a gas expands, it does work on its surroundings by exerting pressure on the walls of its container.
• Since work is done by the gas, its internal energy decreases.

Piston Expansion

Formula: Work Done at Constant Pressure

1. Work done is defined as:

$$\begin{array}{rl}\text{Work Done}& =\text{Force}\times \text{Distance moved in direction of force}\\ W& =F\Delta s\end{array}$$

2. Pressure is defined as:

$$\begin{array}{r}\text{Pressure}=\frac{\text{Force}}{\text{Area}}\\ p=\frac{F}{A}\end{array}$$

3. Rearranging to make force $F$ subject:

$$F=pA$$

4. Substituting into the expression for work:

$$W=pA\times \Delta s$$

5. Area times change in distance is equal to change in volume:

$$W=p\Delta V$$

Examiner Tip: "External" Pressure

The pressure $p$ in the equation $W=p\Delta V$ is the pressure of the surroundings (often atmospheric pressure), not necessarily the internal pressure of the gas itself. This is because when a gas expands, it is doing work against the external environment.

Work Done on a Gas

Work Done on a Gas

• Work is done on a gas when the gas is compressed.
• Since work is done on the gas, its internal energy increases.

Work done on a gas