Gases and work
Section: Thermodynamics | Syllabus: Cambridge AS 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 V Where W is the work done by the gas, p is pressure, and Δ V is the change in volume.
Derivation 1. 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.
Expansion into a Vacuum 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 Gas Diagram 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 Example When 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. Figure 16.4: Area under a pV graph 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. Solution 1. 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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