Viewing as
Teaching this? The teacher view adds 2 files, the mark schemes and the model answers.
Physics · Energy
Efficiency
Calculate efficiency as a decimal or a percentage using energy or power, interpret Sankey diagrams, and describe ways to increase efficiency (Higher tier).
Warm-up
Answer each one, then check.
-
1
What is dissipated energy?
Show answerHide answer
Energy spread to the surroundings in less useful stores
-
2
What is 0.35 as a percentage?
Show answerHide answer
35%
-
3
Write 60% as a decimal.
Show answerHide answer
0.60
-
4
Give the unit of power.
Show answerHide answer
Watt
-
5
What does 'useful' energy mean?
Show answerHide answer
Energy transferred in the way we want
Learning Objectives
- 1Recall and apply the efficiency equations.
- 2Give efficiency as a decimal or a percentage.
- 3Interpret Sankey diagrams.
- 4Describe ways to increase the efficiency of an energy transfer (Higher tier).
EFFICIENCY
efficiency \(= \dfrac{\text{useful output energy transfer}}{\text{total input energy transfer}}\)
Also: efficiency \(= \dfrac{\text{useful power output}}{\text{total power input}}\). Efficiency has no units and is never more than 1 (100%).
A Sankey Diagram
The width of each arrow shows the amount of energy.
Efficiency of a Lamp
A lamp transfers 100 J of electrical energy and 8 J of it is transferred as light. Calculate its efficiency.
Show the solutionHide the solution
- 1 Write the equation efficiency \(= \dfrac{\text{useful output}}{\text{total input}}\)
- 2 Substitute \(\dfrac{8}{100}\)
- 3 Decimal \(0.08\)
- 4 Percentage \(0.08 \times 100 = 8\%\)
AnswerEfficiency \(= 0.08\) or \(8\%\).
Using Power
A motor has a total power input of 500 W and a useful power output of 350 W. Calculate its efficiency as a percentage.
Show the solutionHide the solution
- 1 Substitute \(\dfrac{350}{500}\)
- 2 Decimal \(0.70\)
- 3 Percentage \(70\%\)
Answer70%
Finding the Useful Output
A machine is 85% efficient. How much useful energy does it transfer from a 400 J input?
Show the solutionHide the solution
- 1 Efficiency as a decimal \(0.85\)
- 2 Multiply \(0.85 \times 400 = 340\) J
Answer340 J
Ways to Increase Efficiency (Higher Tier)
Reduce the energy that is dissipated.
-
Lubrication
Reduces friction between moving parts.
-
Thermal insulation
Reduces energy lost by heating, for example around a boiler or a house.
-
Streamlining
Reduces air resistance so less energy is wasted.
-
Better design
For example LED lamps transfer more input energy as light.
-
Higher tier
The question may ask you to suggest a way suitable for a described machine.
Common Mistakes
Check your answer.
-
Efficiency above 1
It cannot be greater than 1 (100%): useful output cannot be more than the input.
-
Wrong way up
Useful output goes on top.
-
Units
Do not write J or W after an efficiency.
-
Percent or decimal
Read the question for the form required.
Compare the Lamps
LED lamp: efficiency 0.85, input power 8 W. Filament lamp: efficiency 0.10, input power 60 W. Calculate the useful power output of each and say which lamp is better.
1. Rearrange the equation for useful power.
2. Compare the two answers.
A good answer shows: LED: 0.85 × 8 = 6.8 W. Filament: 0.10 × 60 = 6.0 W. The LED gives more useful output from far less input, so it is better.
Can I...?
- 1Recall both efficiency equations.
- 2Calculate efficiency.
- 3Convert decimal and percentage.
- 4Interpret a Sankey diagram.
- 5Explain efficiency cannot exceed 1.
- 6Find useful output from an efficiency.
- 7Describe ways to increase efficiency.
- 8Compare devices.
Summary & Exam Focus
- Efficiency = useful output ÷ total input.
- Also useful power ÷ total power.
- Multiply by 100 for a percentage.
- Efficiency is never more than 1.
Exam focus
A device has an input of 400 J and a useful output of 100 J. Calculate the efficiency. (2 marks) (2 marks)
Put useful over total.
Key terms
The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.
- Efficiency
- The fraction of the input energy that is transferred usefully.
- Useful output
- Energy transferred in the way that is wanted.
- Wasted energy
- Energy transferred to stores that are not useful.
- Sankey diagram
- A diagram with arrow widths that show energy amounts.
- Streamlining
- Shaping an object to reduce air resistance.
- Input
- The energy or power supplied to a device.
Practice questions
Have a go at each one before you open its answer.
-
Question 1 Calculate 2 marks
A device transfers 400 J of energy as input and 100 J of useful energy. Calculate the efficiency of the device. Use the equation: efficiency = useful output energy transfer ÷ total input energy transfer
Show answerHide answer
Model answer
\(100 \div 400 = 0.25\) (25%)
Mark scheme
- Correct substitution — 1 mark
- 0.25 or 25% — 1 mark
-
Question 2 Use the diagram 3 marks
The Sankey diagram shows the energy transfers in an electric motor. (a) Calculate the energy wasted every second. (b) Calculate the efficiency of the motor.
Show answerHide answer
Model answer
(a) 300 − 240 = 60 J. (b) 240 ÷ 300 = 0.80 (80%).
Mark scheme
- 60 J — 1 mark
- Correct substitution — 1 mark
- 0.80 or 80% — 1 mark
-
Question 3 Calculate 3 marks
A lamp has an efficiency of 0.20 and a total power input of 60 W. Calculate the useful power output of the lamp.
Show answerHide answer
Model answer
\(0.20 \times 60 = 12\) W
Mark scheme
- Rearranges to power output = efficiency × input — 1 mark
- Correct substitution — 1 mark
- 12 W — 1 mark
-
Question 4 Suggest 2 marks
A car engine wastes a lot of energy. Suggest two ways to increase the efficiency of the car.
Show answerHide answer
Model answer
Any two from: lubricate moving parts to reduce friction; streamline the shape to reduce air resistance; improve insulation or design of the engine to reduce thermal losses.
Mark scheme
- First way — 1 mark
- Second way — 1 mark
-
Question 5 Compare 4 marks
An LED lamp has an efficiency of 0.85 and an input power of 8 W. A filament lamp has an efficiency of 0.10 and an input power of 60 W. Compare the useful power output of the two lamps. Which is the better lamp? Show your calculations.
Show answerHide answer
Model answer
LED: 0.85 × 8 = 6.8 W. Filament: 0.10 × 60 = 6.0 W. The LED lamp transfers more useful power while using far less input power, so it is the better lamp.
Mark scheme
- 6.8 W — 1 mark
- 6.0 W — 1 mark
- LED gives more useful power — 1 mark
- With much less input power — 1 mark
-
Question 6 Explain 2 marks
A student says that a machine has an efficiency of 120%. Explain why this cannot be correct.
Show answerHide answer
Model answer
Useful output cannot be greater than the input because energy cannot be created.
Mark scheme
- Energy cannot be created — 1 mark
- Useful output cannot exceed the total input — 1 mark
Quick check
-
Efficiency is calculated by...
Show answerHide answer
C: useful output ÷ total input
Useful over total.
-
A device is 0.40 efficient. As a percentage this is...
Show answerHide answer
D: 40%
Multiply by 100.
-
A machine takes in 200 J and gives 50 J useful. Efficiency is...
Show answerHide answer
A: 0.25
50 ÷ 200 = 0.25.
-
Which reduces wasted energy in a machine?
Show answerHide answer
B: Lubrication
Lubrication reduces friction.
-
The widths of arrows in a Sankey diagram show...
Show answerHide answer
C: the amount of energy
Wider arrows mean more energy.
Downloads
Free to keep, print and annotate.
Something here looks wrong?
Tell us what and we will go and look. It goes to whoever writes these pages, nobody else, and we do not ask who you are — so there is nothing to sign and nothing comes back to you.