AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Comparison with the theoretical diagrams for these cycles; use of…
Full specification wording
Engine cycles (A-level only): Comparison with the theoretical diagrams for these cycles; use of indicator diagrams for predicting and measuring power and efficiency input power = calorific value × fuel flow rate Indicated power as area of p−V loop × no. of cycles per second × no. of cylinders Output or brake power, P = Tω friction power = indicated power – brake power Engine efficiency; overall, thermal and mechanical efficiencies.
Real indicator diagrams differ from ideal ones: rounded corners, finite combustion time and heat loss reduce the loop area.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 2
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Real indicator diagrams differ from ideal ones: rounded corners, finite combustion time and heat loss reduce the loop area. The loop area gives work per cycle, so indicated power equals area × cycles per second × number of cylinders. Input power comes from calorific value × fuel flow rate. Brake (output) power is measured with a dynamometer using P = Tω, where ω = 2πf. Friction power is indicated power minus brake power. Thermal efficiency compares indicated power with fuel input power, mechanical efficiency compares brake power with indicated power, and overall efficiency combines them (brake power ÷ input power). Work through a numerical example using consistent SI units.
What earns the marks
- Explains that real diagrams have rounded corners and lower peak pressures than theoretical ones because combustion takes time and heat is lost.
- Calculates indicated power as the p−V loop area multiplied by cycles per second and by the number of cylinders.
- Calculates input power as calorific value of the fuel multiplied by the fuel flow rate, converting units such as kW and MJ kg⁻¹ consistently.
- Uses P = Tω with ω = 2πf to find brake power from measured torque and rotational frequency.
- Obtains friction power by subtracting brake power from indicated power.
- Distinguishes thermal efficiency (indicated power ÷ input power), mechanical efficiency (brake power ÷ indicated power) and overall efficiency (brake power ÷ input power).
Common mistakes and how to put them right
Using the wrong area or forgetting the number of cylinders when finding indicated power.
Put it right by multiplying loop area by cycles per second and cylinder count.
Mixing units such as kW, MJ kg⁻¹ and g s⁻¹.
Put it right by converting all quantities to SI before substituting.
Using ω in rev s⁻¹ instead of rad s⁻¹.
Put it right by applying ω = 2πf.
Treating overall efficiency as the sum of thermal and mechanical efficiencies.
Put it right by treating it as their product.
Exam tips
- Write the defining equation before substituting numbers, and state units with every answer.
- Show the conversion of fuel flow rate to kg s⁻¹ and calorific value to J kg⁻¹ explicitly.
- Check that brake power is less than indicated power and that all efficiencies lie between 0 and 1.
Try the lesson
The start of the Engine cycles (A-level only): Comparison with the theoretical diagrams for these cycles; use of indicator diagrams for predicting and measuring power and efficiency input power = calorific value × fuel flow rate Indicated power as area of p−V loop × no. of cycles per second × no. of cylinders Output or brake power, P = Tω friction power = indicated power – brake power Engine efficiency; overall, thermal and mechanical efficiencies. lesson, made from checked teaching notes for this specification point.
Have a go first
Which quantity is obtained by multiplying the area of a p–V loop by the number of cycles per second and by the number of cylinders?
Listen
Real indicator diagrams differ from ideal ones: rounded corners, finite combustion time and heat loss reduce the loop area. The loop area gives work per cycle, so indicated power equals area × cycles per second × number of cylinders. Input power comes from calorific value × fuel flow rate. Brake (output) power is measured with a dynamometer using P = Tω, where ω = 2πf. Friction power is indicated power minus brake power. Thermal efficiency compares indicated power with fuel input power, mechanical efficiency compares brake power with indicated power, and overall efficiency combines them (brake power ÷ input power). Work through a numerical example using consistent SI units. A strong answer earns marks for these points. Explains that real diagrams have rounded corners and lower peak pressures than theoretical ones because combustion takes time and heat is lost. Calculates indicated power as the p−V loop area multiplied by cycles per second and by the number of cylinders. Calculates input power as calorific value of the fuel multiplied by the fuel flow rate, converting units such as kW and MJ kg⁻¹ consistently. Uses P = Tω with ω = 2πf to find brake power from measured torque and rotational frequency. A common slip: Using the wrong area or forgetting the number of cylinders when finding indicated power. Instead, multiplying loop area by cycles per second and cylinder count. Exam tip: Write the defining equation before substituting numbers, and state units with every answer.
Key words
Say what each word means before you turn the card.
Indicated power
Try answering aloud or in your head before turning the card.
Brake power
Try answering aloud or in your head before turning the card.
Friction power
Try answering aloud or in your head before turning the card.
Overall efficiency
Try answering aloud or in your head before turning the card.
See every definition
- Indicated power
- The area of the p−V loop multiplied by the number of cycles per second and by the number of cylinders.
- Brake power
- Output power measured with a dynamometer, given by P = Tω where ω = 2πf.
- Friction power
- The indicated power minus the brake power.
- Overall efficiency
- Brake power divided by input power, combining thermal and mechanical efficiencies.
There is more to this lesson
The full lesson goes on to check your understanding and help you earn the marks. Create a free account to carry on, with your progress saved.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge
Test your understanding of Engine cycles (A-level only): Comparison with the theoretical diagrams for these cycles; use of indicator diagrams for predicting and measuring power and efficiency input power = calorific value × fuel flow rate Indicated power as area of p−V loop × no. of cycles per second × no. of cylinders Output or brake power, P = Tω friction power = indicated power – brake power Engine efficiency; overall, thermal and mechanical efficiencies.
Active recall beats re-reading. Take an instant quiz now to test what you’ve learned and lock it into long-term memory.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge