Kilowatt-Hours (Oxford AQA IGCSE Combined Science Double Award)

Revision Note

Written by: Dan Mitchell-Garnett, Physics Content Creator

Reviewed by: Caroline Carroll, Physics Subject Lead

Units of Energy

Energy measured in joules

Electrical energy transferred is often calculated with units of joules
- One joule is equivalent to one-watt second
Consider an average lightbulb with a power of 60 W, which is left on for 6 hours in a house
- 1 hour is 3600 s
- The electrical energy transferred over this time is 1.296 × 10⁶ J
This number is large and that is one lightbulb for a single day
- A household uses many appliances all year round – the energy transferred per month in joules would be inconveniently large

Energy measured in kilowatt-hours

To make these large values more relatable to daily use:
- Power can be measured in kilowatts (kW)
- Time can be measured in hours (h)
In this case, energy has units of kilowatt-hours (kW h)
- The lightbulb from before receives 3.6 kW h of energy over the 6 hours
- This value is much easier to understand for consumers and energy providers – thinking in terms of hours of use is more practical than seconds

Kilowatt-Hours

As has been stated previously, the equation for energy transferred is:

$E = P \times t$

But here we consider different units:
- E = energy transferred measured in kilowatt-hours (kW h)
- P = power of the appliance measured in kilowatts (kW)
- t = time measured in hours (h)

The usual unit of energy is joules (J), which is one watt-second
To find the number of joules in 1 kW h, convert the power and time to watts and seconds

$1 kW h = 1000 W \times 3600 s = 3.6 \times 10^{6} J$

1000 watts multiplied by 3600 seconds is equal to 1000 multiplied by 3600, in watt-seconds

$1000 W \times 3600 s = 1000 \times 3600 W s = 3.6 \times 10^{6} J$

Therefore, 1 kWh = 3.6 × 10⁶ J
To convert from kW h to J:

$E (kW h) \times (3.6 \times 10^{6}) = E (J)$

To convert from J to kW h:

$E (J) \div (3.6 \times 10^{6}) = E (kW h)$

The kW h is a large unit of energy, and is mostly used for energy in homes, businesses and factories

Worked Example

A cooker transfers 1.2 × 10⁹ J of electrical energy to heat.

Calculate the cost of this if 1 kW h costs 14.2 p.

Here, 100 p = £1 (100 pence = 1 pound).

Answer:

Step 1: List the known quantities

Energy in joules, E (J) = 1.2 × 10⁹ J
Cost per kW h = 14.2 p

Step 2: Convert from J to kW h

$(1.2 \times 10^{9}) \div (3.6 \times 10^{6}) = 333.333 kW h$

Step 3: Calculate the price

$1 kW h = 14.2 p$

$333.333 \times 14.2 = 4733 p = £ 47.33$

Examiner Tip

The equation for energy in kilowatt-hours, with the units of each variable, is given to you on your equation sheet.

You can either memorise the conversions between J and kW h or convert manually, but ensure you are confident in this conversion.

Last updated: 10 April 2024

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