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
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Identify the type of process: Isobaric (constant pressure).
- S2
Use the formula for work done in an isobaric process: W = p × ΔV.
- S3
Calculate the change in volume: ΔV = V final - V initial = 5 m 3 - 2 m 3 = 3 m 3 .
- S4
Substitute the values into the formula: W = 100 kPa × 3 m 3 = 300 kJ.
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Identify the type of process: Isobaric (constant pressure).
- S2
Use the formula for work done in an isobaric process: W = p × ΔV.
- S3
Calculate the change in volume: ΔV = V final - V initial = 5 m 3 - 2 m 3 = 3 m 3 .
- S4
Substitute the values into the formula: W = 100 kPa × 3 m 3 = 300 kJ.
Final answer: 300 kJ
Common mistakes
- Confusing the area under the curve with the change in internal energy. — 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. — 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. — 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. — 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. — 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. — 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
- Full worked solution (all marking points)4 marks