Power and efficiency
Power tells you how quickly energy is transferred. Efficiency tells you what fraction of the energy put in ends up where you wanted it. Both appear in calculation questions and in questions about saving energy at home.
Part 1 of 3: Learn it
In short
- P = E ÷ t: 1 watt is 1 joule per second.
- Efficiency = useful output ÷ total input, using energy or power.
- Wasted energy is usually dissipated as heat to the surroundings.
Where this is in your specification
Spec points: AQA 4.1.1.4, 4.1.2.1 and 4.1.2.2 (Combined Trilogy 6.1.1.4 and 6.1.2), Edexcel Topics 3 and 8, OCR P7.2
| Board | Topic: Energy stores, transfers and efficiency |
|---|---|
| AQA 8463 | 4.1 (8463); 6.1 (8464) |
| Edexcel 1PH0 | Topics 3 and 8 (specific heat capacity: Topic 14) |
| OCR J249 | P7 and P8.2; P5 and P6.2 (specific heat capacity: P1.2) |
| Eduqas C420 | 1.1 to 1.3 |
| Cambridge IGCSE 0625 | 1.7, 2.3 |
| National 5 C857 75 | Dynamics: energy; Properties of matter: specific heat capacity |
Power
P is power in watts (W), E is energy transferred in joules (J), W is work done in joules, and t is time in seconds. Two motors that lift the same load the same height do the same work, but the more powerful one does it faster.
1 kW = 1000 W, so a 2.4 kW kettle transfers 2400 J every second.
Efficiency
It works with energies or with powers, as long as both are the same kind. To give it as a percentage, times the decimal by 100. No real device is 100% efficient, so an answer above 1 (or 100%) means a mistake.
Reducing wasted energy
- Lubricate moving parts to reduce friction.
- Insulate: loft insulation, cavity wall insulation and double glazing slow the transfer of heat out of a house.
- Walls with a lower thermal conductivity, and thicker walls, lose heat more slowly.
Sankey diagrams
A Sankey diagram shows energy transfers as arrows whose widths are in proportion to the amount of energy. The useful arrow carries on, the wasted arrows bend away, and the widths of all the outputs add up to the input.
A device transfers 9000 J in 20 s. What is its power?
Show the answer
9000 ÷ 20 = 450 W.
Part 2 of 3: See it worked
Worked examples
Example 1
A motor transfers 36 000 J in 2 minutes. What is its power?
- t = 2 × 60 = 120 s
- P = 36 000 ÷ 120
Answer: 300 W.
Example 2
A 2.4 kW kettle is on for 3 minutes. How much energy does it transfer?
- P = 2400 W, t = 180 s
- E = P × t = 2400 × 180
Answer: 432 000 J (432 kJ).
Example 3
A lamp is supplied with 60 J and gives out 12 J as light. What is its efficiency?
- Useful output = 12 J, total input = 60 J
- 12 ÷ 60 = 0.2
Answer: 0.2, which is 20%.
Common mistakes
- Using minutes or hours in P = E ÷ t instead of seconds.
- Dividing the input by the output, which gives an efficiency over 1.
- Mixing kW and W in the same calculation.
- Saying wasted energy is destroyed. It is dissipated, spread out into the surroundings.
A machine is 25% efficient and is given 800 J. How much energy is useful?
Show the answer
0.25 × 800 = 200 J.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
A device transfers 9000 J in 20 s. What is its power?
9000 ÷ 20 = 450 W.
A machine is 25% efficient and is given 800 J. How much energy is useful?
0.25 × 800 = 200 J.
Give one way to reduce the wasted energy in a motor.
Lubricate its moving parts to reduce friction.
Jobs that use this
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Full lessons and marked practice for this course are coming soon to Brainlag Learn. See courses