Key Stage 3 science · Physics – Energy

KS3 energy costs: power ratings, kilowatt-hours and bills

In Key Stage 3, children turn everyday energy into numbers. They compare the energy in different foods using the kilojoules on a label, compare the power ratings of appliances in watts and kilowatts, and learn that the energy an appliance transfers depends on both its power and how long it is on. They use this to work out what electricity and other fuels cost in a home, and to compare the fuels and energy resources that supply it.

Fuel uses and energy costs at home, explained

The big idea is that power and energy are different things. Power is how fast an appliance transfers energy, measured in watts (W) or kilowatts (kW), where 1 kW is 1,000 W. Energy is the amount transferred, measured in joules (J) or kilojoules (kJ). The link between them is simple: energy transferred = power × time. A 2,000 W heater transfers 2,000 joules every second it is switched on, which shows how small a joule is for everyday household use.

Because joules are so small, electricity bills use a bigger unit, the kilowatt-hour (kWh). One kilowatt-hour is the energy transferred by a 1 kW appliance running for 1 hour, which is 3,600,000 J or 3,600 kJ. Your child will learn to multiply the power in kilowatts by the time in hours to get kilowatt-hours, then multiply by the price per kilowatt-hour to get the cost. Converting units carefully, such as minutes to hours or watts to kilowatts, is where most of the marks and mistakes are.

Children also meet energy in food. Labels give the energy in kilojoules (kJ), and often in kilocalories (kcal) as well, usually per 100 g and sometimes per portion. Pupils compare labels to see which foods transfer more energy to the body, and connect this to the idea that a body needs a certain amount of energy each day. They are comparing numbers and units, not being asked to count what they eat, and lessons keep the focus on the science rather than on dieting.

Domestic fuel bills bring these ideas together. Homes use electricity, mains gas, heating oil or solid fuels, and children look at where each comes from. Gas bills are also charged per kilowatt-hour, so the same sums work for gas as for electricity. Fossil fuels (coal, oil and natural gas) and nuclear fuel are finite resources, while wind, solar, hydroelectric, tidal, geothermal and biomass can be renewed. Schools choose how deeply to compare them, but pupils should be able to give a reason for and against each, such as cost, reliability and effect on the environment. Wind and solar, for example, depend on the weather.

Words your child will hear

Power: How quickly energy is transferred. Measured in watts (W) or kilowatts (kW).
Watt (W): The unit of power. 1 watt means 1 joule transferred every second.
Kilowatt (kW): 1,000 watts. A kettle might be rated at about 3 kW.
Joule (J): The unit of energy. A kilojoule (kJ) is 1,000 joules.
Kilowatt-hour (kWh): The energy transferred by a 1 kW appliance in 1 hour. The unit electricity is sold in.
Fossil fuel: A fuel such as coal, oil or natural gas, formed over millions of years and not replaced once used.
Renewable resource: An energy resource that is replenished naturally, such as wind, solar or tidal power.

What the National Curriculum says

The programme of study for Key Stage 3 says:

Pupils should be taught about comparing energy values of different foods (from labels) (kJ)
Pupils should be taught about comparing power ratings of appliances in watts (W, kW)
Pupils should be taught about comparing amounts of energy transferred (J, kJ, kW hour)
Pupils should be taught about domestic fuel bills, fuel use and costs
Pupils should be taught about fuels and energy resources

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

A 2 kW electric heater is on for 3 hours. Electricity costs 25p per kWh (a round price chosen to keep the sums easy; real prices change). How much energy does the heater transfer, what does it cost, and how many joules is that?

Check the units. The power is already in kilowatts (2 kW) and the time is in hours (3 h), so the answer will come out in kilowatt-hours.

Use energy transferred = power × time.

energy = power × time
       = 2 kW × 3 h
       = 6 kWh

Cost = number of kWh × price per kWh. Change the pence to pounds at the end.
```
cost = 6 × 25p
     = 150p
     = £1.50
```
To find the joules, use watts and seconds instead. 2 kW is 2,000 W, and 3 hours is 3 × 60 × 60 = 10,800 s.
```
2,000 W × 10,800 s
= 21,600,000 J
= 21,600 kJ
```
Check: 1 kWh is 3,600 kJ, and 6 × 3,600 = 21,600 kJ, so both routes agree. For comparison, a 10 W LED bulb is 0.01 kW, so over the same 3 hours it uses 0.03 kWh and costs 0.75p.

The heater transfers 6 kWh (21,600 kJ) and costs £1.50 at 25p per kWh. It would take the LED bulb 600 hours to use the same energy.

Common mistakes and how to help

Treating kilowatts and kilowatt-hours as the same thing

The names are similar and both appear on appliances and bills, so children write “the kettle uses 3 kWh” when they mean it is rated at 3 kW.

What helps: Say it as a rate and an amount: kW is how fast, kWh is how much. A car’s speed in miles per hour is a rate; the miles travelled are an amount. Ask “for how long?” whenever a power is mentioned.

Thinking the appliance with the biggest power rating always costs the most to run

Children compare the watts on the label and forget the time. A 3 kW kettle looks far hungrier than a 100 W television.

What helps: Work both out. The kettle running for 3 minutes is 3 kW × 0.05 h = 0.15 kWh. The television on for 5 hours is 0.1 kW × 5 h = 0.5 kWh, over three times as much.

Forgetting to convert units before multiplying

Mixing 2,000 W with hours, or 30 minutes with kilowatts, gives answers that are out by a factor of 1,000 or 60.

What helps: Write the units beside every number, and decide first whether the answer should be in kWh (kilowatts and hours) or joules (watts and seconds). Estimate whether the final cost is sensible.

Believing renewable energy is always available, or that fossil fuels are the only reliable choice

“Renewable” sounds like “unlimited”, and children hear one-sided arguments in the news.

What helps: Ask for one advantage and one disadvantage of each resource. Solar panels give nothing at night, and a gas power station releases carbon dioxide when it burns fuel, so the choice is always a trade-off.

How to help at home

Read the labels. Look at the power rating on the back or base of a few appliances, such as a kettle, toaster, lamp and hairdryer. Your child can put them in order, then guess which cost the most to run over a week before working it out.
Check a real bill together. Find the price per kWh on an energy bill or statement and pick one appliance. Let your child work out what an hour of use costs. Seeing real numbers makes the unit price feel meaningful, and you do not need to share the account details.
Compare snack labels. Choose two or three snacks and compare the kJ per 100 g, then the kJ in the portion actually eaten. Ask why those two answers can disagree. The aim is learning to read the label, not judging the food.
Hunt for standby. Walk round the house with your child and spot the small lights that show devices are on standby. Talk about whether they transfer energy all day and what you could switch off safely. Leave anything you are unsure about alone.
Weigh up a fuel. Pick one energy resource, such as wind or natural gas, and ask your child for two reasons for using it and two against. Encourage a reason about cost or reliability, not just “it is green” or “it is bad”.

Leads on to

Key Stage 4: Energy stores, transfers and power
Key Stage 4: Efficiency and energy resources