Kilowatt-Hours (Oxford AQA IGCSE Physics)

Revision Note

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 space equals space P space cross times space 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 space kW space straight h space equals space 1000 space straight W space cross times space 3600 space straight s space equals space 3.6 space cross times space 10 to the power of 6 space straight J

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

1000 space straight W space cross times space 3600 space straight s space equals space 1000 space cross times space 3600 space straight W space straight s space equals space 3.6 space cross times space 10 to the power of 6 space straight J

  • Therefore, 1 kWh = 3.6 × 106 J

  • To convert from kW h to J:

space E space open parentheses kW space straight h close parentheses space space cross times space left parenthesis 3.6 space cross times space 10 to the power of 6 right parenthesis space equals space E open parentheses straight J close parentheses

  • To convert from J to kW h:

E open parentheses straight J close parentheses space space divided by space left parenthesis 3.6 space cross times space 10 to the power of 6 right parenthesis space equals space E open parentheses kW space straight h close parentheses

  • 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

left parenthesis 1.2 space cross times space 10 to the power of 9 right parenthesis space divided by space left parenthesis 3.6 space cross times space 10 to the power of 6 right parenthesis space equals space 333.333 space kW space straight h

Step 3: Calculate the price

1 space kW space straight h space equals space 14.2 space straight p

333.333 space cross times space 14.2 space equals space 4733 space straight p space equals space £ 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.

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