Efficiency — AQA GCSE Physics
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Efficiency explained
Efficiency measures how much of the energy supplied to a device is transferred usefully rather than wasted.
Read the full explanation
For any energy transfer, identify the total input energy transfer and the useful output energy transfer, both measured in joules (J). The useful output is the energy transferred to the intended store or pathway, while the rest is dissipated, often by heating the surroundings. Efficiency is usually expressed as a decimal or percentage. For example, a lamp receiving 100 J of electrical energy and transferring 20 J as light has an efficiency of 0.20 or 20%. The equation applies to all energy transfers, including mechanical, electrical and thermal processes, provided the same unit is used for both energies.
efficiency = useful output energy transfer / total input energy transfer
This equation defines efficiency as the ratio of useful output energy transfer to total input energy transfer. Both quantities are energies measured in joules (J), so efficiency is a dimensionless number. To use the equation, first identify the total energy supplied to the device and the energy transferred usefully. Then divide the useful output by the total input. For example, if a motor is supplied with 500 J and transfers 350 J usefully, efficiency = 350 J / 500 J = 0.70, or 70%. The remaining 150 J is wasted, often transferred by heating. Efficiency can be written as a decimal or multiplied by 100 to give a percentage. The equation applies to any energy transfer, including electrical, mechanical and thermal processes.
Efficiency may also be calculated using the equation:
Efficiency compares the useful energy or power transferred by a device with the total energy or power supplied to it. The word 'also' signals that this is an alternative route: you can calculate efficiency from power values instead of energy values. Power is the rate of energy transfer, so dividing useful power output by total power input gives the same fraction as dividing useful energy output by total energy input, provided the device operates steadily. For example, a motor drawing 500 W from the mains and delivering 350 W of useful mechanical power has efficiency 350 ÷ 500 = 0.70, or 70%. The remaining 150 W is wasted, mainly by heating the surroundings. Because the useful output can never exceed the total input, efficiency is always between 0 and 1, or between 0% and 100%.
efficiency = useful power output / total power input
This equation defines efficiency as the fraction of the total power supplied to a device that is transferred usefully. Power is measured in watts, so if a lamp takes 60 W from the supply and radiates 12 W as useful light, its efficiency is 12 ÷ 60 = 0.20, which is 20%. The other 48 W is wasted, mostly heating the lamp and surroundings. Because energy is conserved, the useful power output cannot exceed the total power input, so efficiency lies between 0 and 1, or between 0% and 100%. A device with efficiency 0.20 converts one fifth of the supplied power into the intended form; the rest is dissipated. The same numerical value is obtained whether you use power or energy, because power is energy transferred each second.
Students should be able to recall and apply both equations.
Efficiency compares the useful energy or power transferred by a device with the total energy or power supplied to it. The two equations are efficiency = useful output energy transfer ÷ total input energy transfer and efficiency = useful power output ÷ total power input. Because efficiency is a ratio of two quantities measured in the same unit, the units cancel, so efficiency has no unit. Recall means writing either equation from memory; apply means substituting values correctly, including converting a percentage to a decimal or the reverse. For example, a motor supplied with 500 J that transfers 350 J usefully has efficiency 350 J ÷ 500 J = 0.70, which is 70%.
Students may be required to calculate or use efficiency values as a decimal or as a percentage.
Efficiency can be expressed as a decimal between 0 and 1 or as a percentage between 0% and 100%. The two forms carry the same information: 0.25 and 25% both mean that one quarter of the input is transferred usefully. To change a decimal to a percentage, multiply by 100; to change a percentage to a decimal, divide by 100. Questions may give efficiency in one form and expect an answer in the other, or may require you to use the value to find a missing energy or power. For example, a lamp with efficiency 0.20 supplied with 300 J transfers 0.20 × 300 J = 60 J usefully, leaving 240 J wasted. A device that is 45% efficient and receives 800 W delivers 0.45 × 800 W = 360 W usefully.
(HT only) Students should be able to describe ways to increase the efficiency of an intended energy transfer.
Efficiency compares useful output energy with total input energy. To improve it, reduce unwanted transfers, mainly by heating, friction and sound. For a filament lamp, only a small fraction of input energy becomes light; most is wasted by heating. Replacing it with an LED increases the useful light output for the same input, so efficiency rises. For a moving machine, lubricating surfaces reduces friction, so less input energy becomes thermal energy in the surroundings. Streamlining a vehicle lowers drag, so less energy is transferred to the air. Insulating a hot water tank reduces heating of the surroundings. In each case, identify the intended useful store or pathway, then reduce the unwanted transfers without reducing the useful output. Higher-tier students should describe these changes clearly and link them to the efficiency equation.
Your focus
- Identify the total input energy transfer and the useful output energy transfer in a described process.
- Apply the efficiency equation to calculate efficiency as a decimal or percentage.
- Interpret an efficiency value to describe how much energy is transferred usefully and how much is wasted.
Show all 21 objectives
- Recall and apply the equation linking efficiency, useful output energy transfer and total input energy transfer.
- Calculate efficiency from given energy values and express it as a decimal or percentage.
- Use the equation to find a missing useful output or total input energy transfer when efficiency is known.
- Select the useful power output and total power input from given data.
- Apply efficiency = useful power output ÷ total power input to obtain a decimal or percentage.
- Interpret an efficiency value and identify the wasted power as the difference between input and useful output.
- Recall and apply the equation efficiency = useful power output ÷ total power input.
- Calculate efficiency from power data and express it as a decimal or percentage.
- Explain, using conservation of energy, why efficiency is always less than or equal to 1.
- Recall both efficiency equations accurately from memory.
- Apply either equation to numerical data involving energy transfers or power transfers.
- Convert fluently between decimal and percentage forms of efficiency and interpret the result in context.
- Convert confidently between decimal and percentage forms of efficiency.
- Use a given efficiency to calculate useful output, total input or wasted transfer.
- Judge whether a calculated efficiency is physically reasonable and present it in the required form.
- Identify the useful and wasted energy transfers in a given device or system.
- Describe at least two practical ways to reduce unwanted energy transfers and increase efficiency.
- Explain how a reduction in wasted energy affects the efficiency of an intended energy transfer.
Efficiency exam tips
Marking Points
- State that efficiency compares useful output energy transfer with total input energy transfer for any energy transfer.
- Identify the total input energy transfer as the energy supplied to the device or process, measured in joules (J).
- Identify the useful output energy transfer as the energy transferred to the intended useful store or pathway, measured in joules (J).
- Explain that wasted energy is transferred to less useful stores, often by heating the surroundings, and is not included in the useful output.
- Calculate efficiency as a decimal by dividing useful output energy transfer by total input energy transfer, then multiply by 100 to express it as a percentage.
- Recognise that efficiency has no unit because it is a ratio of two energies in the same unit.
- Write the equation as efficiency = useful output energy transfer ÷ total input energy transfer.
- Substitute the useful output energy transfer and total input energy transfer in joules (J) into the equation.
- Divide the useful output energy transfer by the total input energy transfer to obtain a decimal efficiency.
- Multiply the decimal by 100 to express efficiency as a percentage when required.
- Interpret the result, stating that the remaining energy is wasted, often by heating the surroundings.
- Recognise that efficiency is a ratio and therefore has no unit.
- State that efficiency compares useful output with total input and can be found from power values as well as energy values.
- Identify the useful power output and the total power input from the information given, in watts or consistent power units.
- Substitute correctly into efficiency = useful power output ÷ total power input and evaluate the fraction.
- Express the result as a decimal or as a percentage, and recognise that a value above 1 or 100% is impossible.
- Explain that wasted power is the difference between total power input and useful power output, often transferred to the thermal store of the surroundings.
- Quote or select the equation efficiency = useful power output ÷ total power input.
- Identify the useful power output and total power input with correct values and units.
- Substitute the values into the equation and calculate the efficiency as a decimal or percentage.
- Interpret the result, for example stating that 20% of the input power is transferred usefully.
- Use conservation of energy to explain why efficiency cannot exceed 1 or 100%.
- States the energy equation as efficiency = useful output energy transfer ÷ total input energy transfer.
- States the power equation as efficiency = useful power output ÷ total power input.
- Explains that both quantities in a calculation must use the same unit so the ratio is dimensionless.
- Substitutes values correctly into either equation and evaluates the quotient accurately.
- Converts between decimal and percentage form by multiplying or dividing by 100.
- Interprets the result, for example recognising that an efficiency of 0.70 means 70% of the input is transferred usefully.
- Converts a decimal efficiency to a percentage by multiplying by 100, and a percentage to a decimal by dividing by 100.
- Uses an efficiency value to find useful output by multiplying efficiency by total input.
- Uses an efficiency value to find total input by dividing useful output by efficiency.
- Recognises that efficiency cannot exceed 1 or 100% for a real device and interprets values accordingly.
- Calculates wasted energy or power as the difference between total input and useful output.
- Presents the final value in the form requested, with the percentage symbol where appropriate.
- Identify the intended useful energy transfer and the unwanted transfers in the device or system.
- Describe a specific change that reduces unwanted energy transfer, such as lubrication to reduce friction between moving parts.
- Describe a specific change that reduces unwanted energy transfer, such as streamlining to reduce drag from the surrounding fluid.
- Describe a specific change that reduces unwanted energy transfer, such as thermal insulation to reduce heating of the surroundings.
- Explain that reducing wasted energy increases the proportion of input energy transferred usefully, so efficiency increases.
- Use the efficiency relationship to support the description, for example efficiency = useful output energy transfer ÷ total input energy transfer.
- Compare two designs and state which is more efficient, referring to the useful and wasted transfers.
Examiner Tips
- 💡Underline the useful output energy transfer and the total input energy transfer in the question before substituting values into the equation.
- 💡Show the substitution clearly, including units, then give the final efficiency as a decimal or percentage as requested.
- 💡Check that the calculated efficiency is less than 1 or less than 100%, since wasted energy means the useful output is always smaller than the total input.
- 💡Write the equation exactly as given before substituting numbers, so the numerator and denominator are clear.
- 💡Convert all energy values to joules before dividing, and keep the units in the substitution line to check consistency.
- 💡If the answer is a decimal, decide whether the question asks for a decimal or a percentage, and convert by multiplying by 100 if needed.
- 💡Underline the useful power output and the total power input in the question before substituting, so the fraction is set up correctly.
- 💡Write the equation, then substitute with units, then evaluate; this makes method marks easier to award even if the final value slips.
- 💡Check the size of your answer: an efficiency greater than 1 or 100% means the fraction has been inverted or the wrong values used.
- 💡Write the equation exactly as given, then substitute numbers beneath it so the examiner can follow your working.
- 💡If the answer is a recurring decimal, give it to a sensible number of significant figures, usually two or three, unless told otherwise.
- 💡When asked to improve efficiency, link your suggestion to reducing the wasted power transfer rather than simply repeating the equation.
- 💡Write the equation you will use before substituting numbers, so the examiner can see your method even if the arithmetic slips.
- 💡Check whether the question asks for a decimal or a percentage, and give the answer in that form with the correct symbol where needed.
- 💡Remember that efficiency is a dimensionless ratio; if you mix energy and power values, your calculation will be invalid.
- 💡Underline the form requested, decimal or percentage, before you calculate, and convert at the end if needed.
- 💡When finding a missing input, rearrange the equation first and then substitute, which reduces arithmetic errors.
- 💡Sanity-check your answer: a useful output should be smaller than the total input, and an efficiency should lie between 0 and 1 or 0% and 100%.
- 💡Name the device and the useful energy transfer before describing the improvement, so your answer is focused on the intended transfer.
- 💡Use the phrase 'reduces unwanted energy transfer by heating to the surroundings' or 'reduces energy transferred by friction' to make the mechanism clear.
- 💡If a calculation is required, write the efficiency equation, substitute the energy values with units, and give the answer as a decimal or percentage as appropriate.
- 💡For a 'describe' question, give a sequence of changes and their effects rather than a single vague statement such as 'make it better'.
Common Mistakes
- Using the wasted energy instead of the useful output energy in the numerator; correct this by identifying the useful output energy transfer first and dividing it by the total input energy transfer.
- Forgetting to convert a decimal efficiency to a percentage when asked; correct this by multiplying the decimal by 100 and adding the percentage symbol.
- Mixing units, such as using kilojoules for input and joules for output; correct this by converting both energies to the same unit, usually joules, before dividing.
- Dividing total input energy transfer by useful output energy transfer; correct this by keeping useful output energy transfer as the numerator and total input energy transfer as the denominator.
- Adding wasted energy to the useful output before dividing; correct this by using only the useful output energy transfer in the numerator and the total input energy transfer in the denominator.
- Writing a unit after the efficiency value, such as J; correct this by giving efficiency as a decimal or percentage with no unit.
- Dividing total power input by useful power output instead of the other way round; correct this by keeping the useful output on top of the fraction.
- Forgetting to convert a percentage answer to a decimal, or a decimal to a percentage; correct this by checking whether the question asks for a fraction or a percentage and converting by multiplying or dividing by 100.
- Adding wasted power to the useful output and treating the sum as the input when the input is already given; correct this by using the stated total power input directly.
- Using energy values in joules in place of power values in watts without converting; correct this by ensuring both quantities in the fraction are powers, or by using the energy version of the equation consistently.
- Mixing units, such as kilowatts on top and watts underneath; correct this by converting both quantities to the same unit before dividing.
- Reporting efficiency as a whole number of watts; correct this by recognising that efficiency is a ratio with no unit, expressed as a decimal or percentage.
- Dividing total input by useful output instead of useful output by total input; correct this by checking that the answer is less than 1 for a real device.
- Mixing units, such as dividing energy in joules by power in watts; correct this by converting both quantities to the same type and unit first.
- Writing a percentage value such as 70 without converting when a decimal is required, or writing 0.70 when a percentage is required; correct this by multiplying or dividing by 100 as the question demands.
- Treating a percentage as a decimal without converting, for example multiplying 800 W by 45 instead of by 0.45; correct this by dividing the percentage by 100 first.
- Forgetting to multiply by 100 when a percentage is required, leaving an answer such as 0.45 when 45% is expected; correct this by checking the requested form.
- Assuming efficiency can be greater than 1 or 100%; correct this by remembering that useful output can never exceed total input for a real device.
- Thinking that efficiency can exceed 100%; correct this by stating that useful output energy is always less than total input energy in any real energy transfer.
- Confusing efficiency with power; correct this by explaining that efficiency is a ratio of energies or powers, while power is the rate of energy transfer.
- Suggesting that adding more energy increases efficiency; correct this by explaining that efficiency improves when a greater proportion of the input energy is transferred usefully, not when more energy is supplied.
- Ignoring the intended useful transfer and describing only a reduction in total energy use; correct this by identifying the useful output first, then reducing the unwanted transfers.