Efficiency: The energy efficiency for any energy transfer can be calculated using the equation:

The idea

Efficiency measures how much of the energy supplied to a device is transferred usefully rather than wasted. For any energy transfer, identify the total input energy and the useful output energy, then divide useful output by total input. The result is a fraction or percentage, always between 0 and 1, or 0% and 100%. For example, a lamp takes in 100 J of electrical energy and transfers 20 J as useful light, so efficiency = 20 J ÷ 100 J = 0.20 or 20%. The remaining 80 J is dissipated, often by heating the surroundings. The equation applies to mechanical, electrical, thermal and other transfers, provided the same unit is used for both energies. Efficiency cannot exceed 1 because energy is conserved and some is always dissipated.

What earns the marks

• State the equation as efficiency = useful output energy transfer ÷ total input energy transfer.
• Identify the useful output energy as the energy transferred to the intended store or form, such as light from a lamp or kinetic energy from a motor.
• Identify the total input energy as the energy supplied to the device before any transfer occurs.
• Substitute values with matching units, usually joules, then divide to obtain a decimal or multiply by 100 to obtain a percentage.
• Recognise that efficiency has no unit and must lie between 0 and 1, or between 0% and 100%.
• Explain that wasted energy is not destroyed but transferred to less useful stores, commonly thermal energy in the surroundings.

Common mistakes and how to put them right

• Dividing total input by useful output instead of useful output by total input.

  Put it right by writing the equation first and checking that the answer is less than 1 or 100%.

• Using different units for the two energies, such as joules for input and kilojoules for output.

  Put it right by converting both to the same unit before dividing.

• Treating the wasted energy as the useful output.

  Put it right by identifying the intended useful transfer, for example light rather than heat from a filament lamp.

Exam tips

• Write the equation, then substitute values with units before calculating, so method marks can be awarded even if the arithmetic slips.
• Check whether the question asks for a decimal or a percentage; if a percentage is required, multiply the decimal by 100 and include the % sign.
• Use the answer to judge reasonableness: an efficiency above 100% signals that the values have been reversed or misread.