16.2.1Thermal physics (A Level)
Work Done by a Gas
5 min read 9 parts Lesson 16 of 20 1 quiz Virtual lab
Lesson summary
16.2.1 Work Done by a Gas — AS PHYSICS 9702 notes: Calculate the work done by and on a gas using W = pΔV and the area under a p–V graph.Expansion — the gas pushes a piston outwards and does work on the surroundings, so its internal energy tends to fallCompression — a force pushes…
- Heat engines
- Force on the piston
- Work for a small movement Δx
- Volume change
- Units check
- Pressure used
Section 1 of 9Work and a gas
Expansion
- Expansion the gas pushes a piston outwards and does work on the surroundings, so its internal energy tends to fall
Compression
- Compression a force pushes the piston inwards through a distance, doing work on the gas, so its internal energy and temperature tend to rise
Mechanism
- Mechanism molecules move faster after compression, increasing kinetic energy and temperature
Heat engines
- Heat engines this work turns thermal energy into mechanical work, as in a steam engine
Section 2 of 9Deriving the equation
1Force on the piston
- F = pA for pressure p and piston area A
2Work for a small movement Δx
- FΔx = pAΔx
3Volume change
- AΔx = ΔV
4Result
- W = pΔV at constant pressure
Units check
- Pa × m³ = N m⁻² × m³ = N m = J
Pressure used
- Pressure used p is the external pressure of the surroundings, because the gas does work on them
Section 3 of 9Signs of the work
Signs of the work
Expansion
- ΔV is positive, work is done by the gas, and work done on the gas is w = −pΔV, which is negative
Compression
- ΔV is negative, work is done on the gas, and w = −pΔV is positive
Convention in this course
- ΔU = q + w, with w the work done on the system
Other convention
- Q = ΔU + W with W the work done by the gas and W = +pΔV
Check
- Check expansion should use energy from the gas and compression should add energy to it
Section 4 of 9The p–V graph
1Varying pressure
- Varying pressure split the change into tiny steps of nearly constant p, each with work pΔV equal to the area of a thin strip
2Result
- Result the work done equals the area under the p–V curve between the initial and final volumes
3Direction
- Direction for expansion the graph is traced left to right and for compression right to left
4Closed cycle
- Closed cycle the net work per cycle equals the area enclosed by the loop
- A clockwise loop means net work is done by the gas on its surroundings
Section 5 of 9Where work appears in practice
1Boiling
- Boiling water turning to steam at atmospheric pressure expands about 1600 times and pushes back the atmosphere, using some of the energy supplied
2Bicycle pump
- Bicycle pump work done on the gas warms it
3Spray can
- Spray can the gas expands rapidly, does work and cools because little heat can flow in
4Heat engines
- Heat engines gas expands at high pressure and is compressed at low pressure, giving a net work output per cycle
Section 6 of 9Method
1Find the change in volume
- ΔV = final volume − initial volume, in m³
2
Take the external pressure in Pa
3Calculate the magnitude
- |W| = pΔV
4
Assign the sign from expansion or compression
Section 7 of 9More from the specification
1
First law of thermodynamics
- The increase in internal energy of a closed system equals the heat supplied to the system plus the work done on the system: delta U = q + w.
2
Work done during gas expansion
- When an ideal gas expands at constant pressure p against its surroundings, the work done by the gas is given by W = p delta V.
3
Pressure-volume (p-V) diagrams
- The area under a process curve on a p-V indicator diagram represents the net mechanical work transferred between the gas and its surroundings.
4
First law of thermodynamics
- The increase in internal energy of a closed system equals the heat supplied to the system plus the work done on the system: delta U = q + w.
5
Work done during gas expansion
- When an ideal gas expands at constant pressure p against its surroundings, the work done by the gas is given by W = p delta V.
6
Pressure-volume (p-V) diagrams
- The area under a process curve on a p-V indicator diagram represents the net mechanical work transferred between the gas and its surroundings.
7
First law of thermodynamics
- The increase in internal energy of a closed system equals the heat supplied to the system plus the work done on the system: delta U = q + w.
8
Work done during gas expansion
- When an ideal gas expands at constant pressure p against its surroundings, the work done by the gas is given by W = p delta V.
9
Pressure-volume (p-V) diagrams
- The area under a process curve on a p-V indicator diagram represents the net mechanical work transferred between the gas and its surroundings.
10
Liquid
- State with a fixed volume that takes the shape of its container.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Work done by a gas | energy transferred when the gas expands against an external pressure, W = pΔV |
| Work done on a gas | energy transferred to a gas by compressing it |
| p–V graph | a graph of pressure against volume whose area under the curve is the work done |
| External pressure | the pressure of the surroundings against which the gas works |
| Heat engine | a device using a cycle of a gas to convert thermal energy into work |
| Sign convention | the rule for positive and negative q and w |
Section 9 of 9Exam technique
1
Using the gas pressure instead of the external pressure — the gas does work against its surroundings.
2
Forgetting to convert volumes to m³ — cm³ must be multiplied by 10⁻⁶.
3
Mixing sign conventions — state whether W is by or on the gas.
4
Using W = pΔV when pressure changes — use the area under the p–V graph.