Gases and work
Section: Thermodynamics | Syllabus: Cambridge A Level Physics (9702)
Work Done by an Expanding Gas
When a gas in a cylinder expands, it pushes against the surroundings (e.g., a piston), doing work. If the expansion occurs at constant pressure (p):
W = p Δ VWhere W is the work done by the gas, p is pressure, and Δ V is the change in volume.
Derivation1. Force exerted by gas: F = p × A (where A is piston area).
2. Work done: W = F × Δ s (where Δ s is displacement).
3. Substitute F: W = (pA) × Δ s = p × (A Δ s).
4. Since A Δ s is the change in volume Δ V: W = p Δ V.
When a gas expands into a vacuum (free expansion), it does zero work (W = 0). This is because there is no external pressure or particles to push against, so no force is exerted.
Figure 16.3: Expansion of a GasDiagram of a piston moving outward, increasing the volume of the trapped gas and doing work against the external atmosphere.
Doing Work ON a Gas
The Bicycle Pump ExampleWhen you use a bicycle pump, you apply a force to compress the air inside. You are doing work on the gas. This work increases the internal energy of the air molecules, which is why the end of the pump feels warm to the touch.
pV Diagrams
A graph of pressure (p) against volume (V) is called a pV diagram. The area under the graph represents the work done by or on the gas.
- Expansion: Arrow points to the right. The gas does work.
- Compression: Arrow points to the left. Work is done ON the gas.
A pV graph showing a shaded area under a curve, representing the work done during a volume change from V_1 to V_2.
Worked Examples
Worked Example: Helium Expansion (Q6)Question: Helium expands at a constant pressure of 250 kPa. The initial volume is 0.205 m^3 and the gas does 1.55 kJ of work against surroundings. Calculate the final volume.
Solution1. W = p Δ V Δ V = W / p.
2. Δ V = 1550 / 250000 = 0.0062 m^3.
3. Final Volume V_f = V_i + Δ V = 0.205 + 0.0062 = 0.211 m^3.
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