A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Work Done in p-V Diagrams and Cyclic Processes — mark scheme explained
The short answer
In AQA A-Level Physics, understanding the representation of processes on a pressure-volume (p–V) diagram is crucial for grasping how work is done by or on a gas. This topic also extends to cyclic processes, where the area enclosed by the loop represents the net work done per cycle. 1.
The question
A gas undergoes an isobaric process where its volume increases from 2 m 3 to 5 m 3 at a constant pressure of 100 kPa. Calculate the work done by the gas.
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For questions involving p-V diagrams, marks are typically awarded for correctly identifying processes, accurately estimating or calculating areas, and providing correct units. Ensure your working is clear and logical.
What the command words demand
- Identify
- Recognize and name different processes (isobaric, isochoric, isothermal, adiabatic) on a p–V diagram.
- Estimate
- Calculate the work done by or on the gas using the area under the curve on a p–V diagram.
- Calculate
- Determine the net work done in a cyclic process by finding the area of the loop.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 5-7 minutes for a typical question on this topic, depending on the complexity of the diagram and calculations required.
- Identify the type of process: Isobaric (constant pressure).0 marks
- Use the formula for work done in an isobaric process: W = p × ΔV.1 mark
- Calculate the change in volume: ΔV = V final - V initial = 5 m 3 - 2 m 3 = 3 m 3 .1 mark
- Substitute the values into the formula: W = 100 kPa × 3 m 3 = 300 kJ.2 marks
Final answer: 300 kJ
Work through every step correctly and you earn all 4 marks.
Another worked example
A gas undergoes a cyclic process as shown on the p-V diagram. The initial and final states are the same, and the loop is enclosed by points A, B, C, and D. Calculate the net work done per cycle if the area of the loop is 150 J.
- Identify that this is a cyclic process where the system returns to its initial state.0 marks
- Recall that the net work done in a cyclic process is equal to the area enclosed by the loop on the p-V diagram.2 marks
- The area of the loop is given as 150 J, so the net work done per cycle is 150 J.1 mark
Final answer: 150 J
Work through every step correctly and you earn all 3 marks.
Common mistakes
Confusing the area under the curve with the change in internal energy.
Why it happens: Students sometimes mix up the concepts of work and internal energy. The area under the curve on a p-V diagram represents work done, not the change in internal energy.
Fix: Always remember that the area under the curve on a p-V diagram represents the work done by or on the gas during the process.
Forgetting to use the correct units for pressure and volume when calculating work.
Why it happens: Students may forget to convert units, leading to incorrect calculations. For example, using kPa instead of Pa or m 3 instead of cm 3 can result in significant errors.
Fix: Always check and use consistent units for pressure (Pa) and volume (m 3 ) when calculating work done.
Misinterpreting the direction of the process on a p-V diagram.
Why it happens: Students may not correctly identify whether the process is expansion (work done by the gas) or compression (work done on the gas). This can lead to incorrect signs for work done.
Fix: Carefully determine the direction of the process. If the volume increases, it's an expansion and work is done by the gas. If the volume decreases, it's a compression and work is done on the gas.
Failing to recognize that no work is done during an isochoric process.
Why it happens: Students may incorrectly assume that any change in state involves work, even when the volume remains constant.
Fix: Remember that no work is done during an isochoric process because there is no change in volume (W = 0).
Incorrectly calculating the area of a loop for cyclic processes.
Why it happens: Students may miscalculate the area enclosed by the loop, leading to incorrect values for net work done per cycle.
Fix: Carefully calculate the area of the loop on the p-V diagram. Use geometric methods or numerical integration if necessary.
Forgetting that the net work done in a cyclic process is equal to the area of the loop.
Why it happens: Students may not fully understand the relationship between the area enclosed by the loop and the net work done per cycle.
Fix: Always remember that the net work done in a cyclic process is equal to the area enclosed by the loop on the p-V diagram.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Work Done | Find the work done by a gas expanding at constant pressure using W = pΔV. | 4 |
| Cyclic Process Work | Find the net work done per cycle from the area enclosed by a p-V loop. | 3 |
| Work From p-V Diagram | Estimate work done by a gas by calculating the area under a straight-line p-V graph. | 4 |
| Calculate Work Done | Find total work done by a gas across isobaric and isochoric stages of a process. | 5 |
| Total across these question types | 16 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.