✅ Useful energy output
The energy that does the job the device was made for. For an electric whisk, it is the energy transferred to the kinetic store of the spinning beaters.
Energy Transfers » Conservation of Energy and Efficiency
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 4.3, 4.4
- The principle of conservation of energy and how to use it
- How to split an energy transfer into useful and wasted energy
- The efficiency equation, which you must learn, and how to rearrange it
- Why efficiency can never be more than 100%
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Unlock This CourseThe principle of conservation of energy
In Energy Stores and Transfers you described energy moving from one store to another. This lesson adds the rule that controls every one of those transfers.
The principle of conservation of energy says: energy cannot be created or destroyed. It can only be transferred from one store to another.
So if you add up all the energy before something happens and all the energy afterwards, the two totals are always the same. Energy never appears from nowhere and it never vanishes.
Think of a child on a playground swing who stops being pushed. The swing gets lower and lower until it stops. It looks as if the energy has gone, but it has not. Air resistance and friction at the top of the chains have transferred it, bit by bit, to the thermal store of the air and the chains. They are very slightly warmer.
Key terms:
- Principle of conservation of energy: energy cannot be created or destroyed, only transferred from one store to another.
- Total energy input: all the energy supplied to a device.
- Useful energy output: the energy transferred to the store we want.
- Wasted energy: the energy transferred to stores we do not want.
- Total energy output: the useful energy output and the wasted energy added together.
- Efficiency: the fraction (or percentage) of the total energy that is transferred usefully.
Useful energy and wasted energy
Almost no device sends all of its energy where we want it. Some nearly always goes somewhere else.
🔥 Wasted energy
The energy that does not do the job. The whisk gets warm and makes a noise. That energy is not destroyed, but it is no use to us.
Because energy is conserved, everything that goes in must come out:
Conservation of energy for a device
total energy input = useful energy output + wasted energy
This also means that the total energy output is equal to the total energy input.
| Device | Useful energy output | Wasted energy |
|---|---|---|
| Sewing machine motor | To the kinetic store of the needle | Heating the motor, sound |
| Radio | Sound | Heating the case and the air around it |
| Petrol lawnmower engine | To the kinetic store of the blades | Heating the engine and exhaust gases, sound |
| Power bank being charged | To the chemical store of its battery | Heating the power bank and the cable |
Where does wasted energy end up? Usually in the thermal store of the surroundings. Friction heats moving parts, a current heats wires, and even wasted sound ends up making the air slightly warmer. The energy spreads out so thinly that it cannot easily be collected and used again. That is why we call it wasted.
Using conservation of energy in calculations
If you know two of the three amounts, you can always find the third by adding or subtracting.
Worked example 1: finding the wasted energy
A sewing machine motor is supplied with 500 J of energy. It transfers 350 J to the kinetic store of the needle. Calculate the wasted energy.
total energy input = useful energy output + wasted energy
wasted energy = total energy input − useful energy output
wasted energy = 500 − 350 = 150 J
Worked example 2: finding the total energy input
A gas boiler transfers 10 800 J usefully to the thermal store of the water. 1200 J is wasted heating the air outside. Calculate the total energy input.
total energy input = useful energy output + wasted energy
total energy input = 10 800 + 1200 = 12 000 J
Efficiency
Efficiency tells you how good a device is at transferring energy usefully. An efficient device wastes very little.
Learn this equation
efficiency = (useful energy output ÷ total energy output) × 100%
This equation is not given in the exam. You must learn it.
The specification says total energy output. Remember that this means useful plus wasted, which is the same number as the total energy input. So if a question gives you the energy supplied to a device, use that as the total.
Efficiency has no unit, because it is one amount of energy divided by another. It is usually written as a percentage. It can also be written as a decimal: 75% is the same as 0.75.
Worked example 3: calculating efficiency
An electric winch is supplied with 2000 J of energy. It transfers 1500 J usefully to lift a boat. Calculate its efficiency.
efficiency = (useful energy output ÷ total energy output) × 100%
efficiency = (1500 ÷ 2000) × 100%
efficiency = 0.75 × 100% = 75%
Worked example 4: when you are given the wasted energy
A petrol lawnmower engine transfers 600 J usefully and wastes 1800 J. Calculate its efficiency.
Step 1: total energy output = 600 + 1800 = 2400 J
Step 2: efficiency = (600 ÷ 2400) × 100% = 0.25 × 100% = 25%
Rearranging the efficiency equation
First change the percentage to a decimal by dividing by 100. Then use one of these.
| To find | Use |
|---|---|
| Efficiency (as a decimal) | useful energy output ÷ total energy output |
| Useful energy output | efficiency × total energy output |
| Total energy output | useful energy output ÷ efficiency |
Worked example 5: finding the useful energy output
The motor of an electric bike is 80% efficient. It is supplied with 450 J. Calculate the useful energy output and the wasted energy.
80% = 0.80
useful energy output = efficiency × total energy output = 0.80 × 450 = 360 J
wasted energy = 450 − 360 = 90 J
Worked example 6: finding the total energy
A stair lift motor is 60% efficient. It must transfer 2400 J usefully. Calculate the total energy that must be supplied.
60% = 0.60
total energy output = useful energy output ÷ efficiency = 2400 ÷ 0.60 = 4000 J
Check: 2400 ÷ 4000 = 0.60, which is 60%.
Why efficiency can never be more than 100%
An efficiency above 100% would mean the useful energy output was bigger than the total energy supplied. The device would be creating energy. The principle of conservation of energy says that cannot happen.
In practice, efficiency is almost always less than 100%, because some energy is nearly always wasted. So if your answer comes out above 100%, or above 1 as a decimal, you have made a mistake. The most likely one is dividing the wrong way up.
Common mistakes
- Saying energy is 'lost' or 'used up'. Energy is never destroyed. Say it is wasted, or transferred to the thermal store of the surroundings.
- Dividing the wrong way up. The useful energy output always goes on top. It is the smaller number.
- Using the wasted energy on top. If a question gives the wasted energy, subtract it from the total first to find the useful energy.
- Forgetting to change a percentage to a decimal before rearranging. Use 0.80, not 80.
- Giving efficiency a unit. It is a percentage or a decimal, never joules.
Exam-style question
An electric motor drives a conveyor belt that moves parcels in a warehouse. In one minute the motor is supplied with 8000 J of energy. It transfers 5200 J usefully to the parcels.
(a) State the principle of conservation of energy. [1 mark]
(b) (i) Calculate the energy wasted by the motor in one minute. [2 marks]
(ii) State where this wasted energy ends up. [1 mark]
(c) Calculate the efficiency of the motor. [3 marks]
(d) The motor is replaced by one with an efficiency of 80%. Calculate the total energy that must be supplied to this motor for it to transfer 5200 J usefully. [3 marks]
(e) A student calculates the efficiency of a different motor as 130%. Explain why this answer must be wrong. [2 marks]
Model answer
(a) Energy cannot be created or destroyed, only transferred from one store to another (1).
(b) (i) wasted energy = total energy input − useful energy output = 8000 − 5200 (1) = 2800 J (1).
(ii) In the thermal store of the surroundings (1).
(c) efficiency = (useful energy output ÷ total energy output) × 100% (1) = (5200 ÷ 8000) × 100% (1) = 65% (1).
(d) 80% = 0.80 (1). total energy = useful energy output ÷ efficiency = 5200 ÷ 0.80 (1) = 6500 J (1).
(e) It would mean the useful energy output is greater than the total energy supplied (1). Energy cannot be created, so this is impossible (1).
Exam tip
In part (c), write the equation in words before you put any numbers in. It earns the first mark even if you then slip on the calculator. Then check your answer makes sense: 5200 J is more than half of 8000 J, so the efficiency should be a bit above 50%, and it must be below 100%.