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Kilowatt-hours

Energy and power · level 4, lesson 3 of 6

A question to start

An electricity bill does not count joules. It counts "units", or kWh. What is a kWh, and how many joules is it?

The idea

A joule is so small that a home uses millions of them every hour. So electricity is measured in a bigger unit, the kilowatt-hour, kWh:

1 kWh is the energy used by something of 1 kW running for 1 hour.

\[1 \text{ kWh} = 1000 \text{ W} \times 3600 \text{ s} = 3{,}600{,}000 \text{ J} = 3.6 \text{ MJ}.\]

To find the energy in kWh: kilowatts × hours.

Appliance Power Time Energy
LED lamp 0.008 kW 5 hours 0.04 kWh
Kettle 2 kW 3 minutes (0.05 h) 0.1 kWh
Oven 2.5 kW 1 hour 2.5 kWh
Electric heater 2 kW 8 hours 16 kWh
1 kW heater for 1 hour2 kW kettle for half an hour100 W bulb for 10 hours=

All three bars are the same energy: 1 kWh. A home in the United States used on average about 30 kWh a day in 2022, 10,791 kWh in the year.

On Mars, a habitat's engineers would count energy in kWh too, and plan how many kWh the panels or power unit make in a sol and how many the habitat needs.

Worked examples

1. kWh to joules. 2.5 kWh \(= 2.5 \times 3.6 = 9\) MJ.

2. A laptop. 50 W is 0.05 kW. Four hours: \(0.05 \times 4 = 0.2\) kWh.

3. A bill. At 15 cents a kWh, the heater above for 8 hours costs \(16 \times 15 = 240\) cents.

Try it

  1. How many joules are in 1 kWh?
  2. A 3 kW oven runs for 40 minutes. How many kWh does it use?
  3. Change 18 MJ into kWh.
  4. A habitat's panels make 50 kWh in a sol. How many hours could they run a 2 kW heater?
Answers
  1. 3,600,000 J (3.6 MJ).
  2. \(3 \times \tfrac{2}{3} = 2\) kWh.
  3. \(18 \div 3.6 = 5\) kWh.
  4. \(50 \div 2 = 25\) hours.

Common mistake

"kWh means kilowatts per hour." It is kilowatts times hours: a power multiplied by a time, which gives an energy.

Where it leads