The shape of the lesson
By the end of the lesson, learners can
- Useful out, wasted away: Adjust the input energy and how much is wasted.
- The useful fraction: The defining equation, the power form, and the rearrangement for useful output:
- Energy form: useful energy output ÷ total energy input.
- Power form: useful power output ÷ total power input.
- Sankey: arrow width is proportional to the energy it carries.
One picture every idea returns to
Efficiency = useful energy output ÷ total energy input (× 100%). Equivalently, efficiency = useful power output ÷ total power input (× 100%). On a Sankey diagram, it is the useful branch as a fraction of the whole.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, How much actually does the job.. Every machine wastes some of the energy it is given, usually as heat to the surroundings. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Useful out, wasted away | Adjust the input energy and how much is wasted. Project tab 6 of the lab (Efficiency) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: The useful fraction | The defining equation, the power form, and the rearrangement for useful output: Model the worked example Worked example on the board, one line at a time. | Round Table |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 13 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in The useful fraction, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Round Table
One sheet travels round the team. Each student adds one line of working or one idea and passes it on, so the solution is built four hands at a time and every contribution is visible.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Keep both terms the same kind. | Divide energy by energy, or power by power, never a mixture of the two. Put the useful amount on top and the total input on the bottom, and remember to multiply by 100 if a percentage is asked for. A bare ratio above 1 means you have flipped the fraction. |
Efficiency: worksheet
6 questions, 13 marks. Written in the style of the papers; no past paper question is reproduced.
Write the two equivalent equations for efficiency, one using energy and one using power.
A machine is given 400 J of energy and usefully transfers 240 J. Calculate its efficiency as a percentage.
A lamp has a power input of 60 W and produces 9.0 W of light. Calculate its efficiency.
A device is supplied with 800 J of energy and is 25% efficient. Calculate the useful energy output and the energy wasted.
A Sankey diagram for a motor shows 1000 J flowing in and 400 J of useful output. State the energy wasted and describe how the widths of the useful and input arrows compare.
Explain why no real device can be 100% efficient.
Answer key and marking notes
- efficiency = useful energy output ÷ total energy input (× 100%). ✓
- efficiency = useful power output ÷ total power input (× 100%). ✓
- efficiency = 240 ÷ 400 = 0.60
60 %
- efficiency = useful power ÷ total power = 9.0 ÷ 60
15 %
power over power, not power over energy
- useful = 0.25 × 800 = 200 J
wasted = 800 − 200 = 600 J
useful 200 J, wasted 600 J
- Wasted energy = 1000 − 400 = 600 J. ✓
- The useful arrow is narrower than the input arrow, with its width 400/1000 of the input, since width is proportional to energy. ✓
- Some energy is always transferred to a non-useful store, usually the thermal store, by friction, resistance or sound. ✓
- So the useful output is always less than the total input, giving an efficiency below 100%. ✓
3 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
A motor is supplied with 800 J of energy and usefully transfers 600 J. What is its efficiency?
- A25%
- B75%
- C133%
- D140%
A lamp has a power input of 60 W and a useful light power output of 9.0 W. What is its efficiency?
- A6.7%
- B15%
- C51%
- D85%
A machine is described as being 100% efficient. Why is this impossible for a real machine?
- ASome input energy is always dissipated, usually to the thermal store.
- BEnergy is destroyed inside the machine.
- CThe useful output is always greater than the input.
- DMachines do not transfer energy at all.
Quiz key
efficiency = 600 ÷ 800 × 100 = 75%. Option A gives the percentage wasted (200 ÷ 800); C inverts the fraction. Efficiency can never exceed 100%, which rules out C and D.
efficiency = 9.0 ÷ 60 × 100 = 15%. Option D (85%) is the percentage wasted as heat; A inverts the fraction.
Real machines always dissipate some energy, often as heat from friction, to the surroundings, so the useful output is always less than the input. Energy is not destroyed (ruling out B), and the output can never exceed the input (ruling out C).
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.