Conservation and power
Account for every energy output with conservation of energy, and calculate power from energy and time.
On this page
Energy · about 25–35 min
What you need to understand
Joules measure energy. Watts measure power: 1 W = 1 J/s.
Definitions
- conservation of energy
the principle that energy cannot be created or destroyed, although it can be transferred
For example: Useful and unwanted outputs together account for the input energy.- power
the energy transferred each second
For example: A 30 W lamp transfers 30 J each second.
Key idea
- LookA lamp transfers 1,800 J in 60 s. Calculate its power.
- ThinkJoules measure energy. Watts measure power: 1 W = 1 J/s.
- DoAccount for useful and other transfers, and calculate power in watts from energy in joules and time in seconds.
Review the full energy topic picture
Explanation
Conservation of energy means that the total input equals all the outputs. A useful output is only part of the account. For a lamp, light may be useful, but the thermal transfer still counts.
Power tells us how quickly energy is transferred. Calculate it using power = energy transferred ÷ time. A device that transfers 1,800 J in 60 s has a power of 30 W because it transfers 30 J each second.
Pause and say it: Joules measure energy. Watts measure power: 1 W = 1 J/s.
Common mistake
Tempting wrong idea: Useful output is added to total input when finding the other transfers.
Why it fails: The input is all the energy supplied, and the useful output is already part of it. The other transfers are what is left, input − useful output. Adding the two counts the useful energy twice.
Use this instead: Adding input and output double-counts energy; calculate 800 − 250.
Practical work
What to show: Account for useful and other transfers, and calculate power in watts from energy in joules and time in seconds.
Before you finish: Useful and other outputs must both be included.
Practical link: The topic investigation is taught in “Follow an energy transfer”
6. Worked Examples
Modelled example 1
Power of a lamp
Problem
A lamp transfers 1,800 J in 60 s. Calculate its power.
Study the worked solution
Reason from the evidence
Method
Use power as the energy transferred during each second.
Reason
Dividing joules by seconds gives joules per second, which is measured in watts.
Working
- Use power = energy transferred ÷ time.
- P = 1,800 J ÷ 60 s.
- P = 30 J/s = 30 W.
State the conclusion
Working
The lamp’s power is 30 W.
Guided practice 2
Account for a motor’s input
Problem
A motor receives 2,400 J in 80 s. It transfers 1,700 J usefully. Find its power and the energy transferred in other ways.
Calculate both missing quantities
Hints
Hint 1: find the rate
Divide the total energy transferred by the time.
Hint 2: complete the account
Subtract useful output from total input.
View solution step by step
Calculate the power
Method
Use the complete 2,400 J transfer when finding the motor’s power.
Reason
Power is the total rate of energy transfer, not only the useful rate.
Working
power = 2,400 J ÷ 80 s = 30 WAccount for the other transfers
Reason
Conservation requires all outputs to add to the input.
Working
other transfers = 2,400 J − 1,700 J = 700 J
Common misconception 3
Correct a power calculation
Learner response
For 500 J transferred in 10 s, a learner writes “power = 500 × 10 = 5,000 W”. Spot and correct the first error.
Use meaning and units to correct the method
View solution step by step
Return to the meaning of power
Method
Divide the energy among the 10 seconds.Reason
Power asks how many joules are transferred in each second.
Working
power = 500 J ÷ 10 s = 50 J/s = 50 W
Examiner practice 4
Power and conservation in a lift motor
Examination question
A lift motor transfers 1,200 J in 40 s. Of this, 900 J is transferred usefully. Calculate the motor’s power and the energy transferred in other ways. [4 marks]
Show both relationships and answers
View solution step by step
Use the power relationship
2 marksMethod
Divide total transferred energy by time.Reason
The question asks for the motor’s overall transfer rate.
Working
power = 1,200 J ÷ 40 s = 30 WApply conservation
2 marksMethod
Subtract useful output from the total input.Reason
The remaining energy must still be accounted for.Working
other transfers = 1,200 J − 900 J = 300 J
Self-mark with the mark scheme
Compare your response with each mark point. Select a point only when your response contains that evidence.
Self-mark the power method, power answer, conservation method and remaining energy separately.
Challenge 5
Compare devices from a data table
Problem
Two mixers each transfer 3,600 J. Mixer A takes 45 s and Mixer B takes 90 s. Without assuming either transfers more total energy, determine which is more powerful and by what factor.
Compare both rates
Hints
Hint 1: calculate each rate
Use the same 3,600 J with each time.
Hint 2: compare as a factor
Divide the larger power by the smaller power.
View solution step by step
Find both powers
Method
Convert each row into energy transferred per second.
Reason
Equal energy does not mean equal power when the times differ.
Working
A: 3,600 ÷ 45 = 80 W; B: 3,600 ÷ 90 = 40 WState the comparison
Working
Mixer A is twice as powerful as Mixer B, although both transfer 3,600 J in total.
Guided practice
Try it with support
A motor receives 600 J and transfers 420 J usefully. Account for the remaining energy, then find its power if the transfer takes 20 s.
Use input = useful + other transfers.
Then divide total transferred energy by time.
Check the guided answer
Answer: The other transfers total 180 J. The motor’s power is 600 J ÷ 20 s = 30 W.
Check: Energy is in joules; power is in watts or joules per second.
Practise and continue
Practise this
A lamp transfers 900 J in 30 s. Calculate its power and explain why a warm lamp does not break conservation of energy.
Need a hint?
Power = energy ÷ time.
Check your answer
Answer: Its power is 30 W. The warming is another output transfer, so it belongs in the complete energy account.
Check: Useful and other outputs must both be included.
Think like a scientist
Why should an energy-flow diagram show an arrow to the surroundings?
Check the reasoning
The arrow represents energy transferred to the surroundings, often thermally or as sound, so the diagram accounts for the whole input.
Remember: A model is useful only when its boundary and omitted details are understood.
One-minute check
Hide the page and explain account for energy and compare power in your own words.
Give a new example that is different from the worked example.
Correct this common mistake: “Useful output is added to total input when finding the other transfers.”
Syllabus and review details
- SEC G1 Science 2027 · 2027
Content structure and syllabus content, PDF pages 8–17
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