What you'll learn
Energy is never destroyed, but it often ends up in forms we cannot use. This revision guide covers how to calculate the efficiency of energy transfers and understand why no device can ever be 100% efficient. You'll learn the equations, develop your calculation skills, and master the exam technique needed to score full marks on efficiency questions.
Key terms and definitions
Efficiency — the proportion of energy supplied to a device that is usefully transferred, expressed as a decimal, percentage or fraction
Useful energy — energy transferred to where it is wanted in the form that is needed
Wasted energy — energy that is not usefully transferred or transformed, usually dissipated to the surroundings by heating and radiation
Dissipation — the spreading out of energy to the surroundings, making it less useful (often as thermal energy)
Input energy — the total energy supplied to a device or system
Output energy — the total energy transferred by a device or system (includes both useful and wasted energy)
Sankey diagram — a visual representation of energy transfers showing the flow and relative amounts of useful and wasted energy
Power — the rate of energy transfer measured in watts (W), where 1 watt = 1 joule per second
Core concepts
Understanding energy transfers and waste
Every energy transfer involves some energy being dissipated to the surroundings in a way that makes it less useful. Most commonly, this occurs through:
- Friction between moving parts, which causes heating of the surfaces and surroundings
- Air resistance acting on moving objects, transferring kinetic energy to thermal energy in the air
- Electrical resistance in wires and components, causing heating
- Sound produced by vibrating parts (though sound itself eventually dissipates as thermal energy)
These dissipated energy stores spread out into the surroundings, increasing the thermal energy of the environment. While this energy still exists (energy is conserved), it becomes increasingly difficult to use for further energy transfers. This is why we describe it as "wasted."
Key principle: The total energy output always equals the total energy input (conservation of energy), but not all output energy is useful.
The efficiency equation
The AQA GCSE Physics specification requires you to know and apply the efficiency equation in two forms:
Efficiency = useful energy transferred by the device ÷ total energy supplied to the device
Or in terms of power:
Efficiency = useful power output ÷ total power input
Efficiency has no units because it is a ratio. It can be expressed as:
- A decimal between 0 and 1 (e.g., 0.85)
- A percentage between 0% and 100% (e.g., 85%)
- A fraction (e.g., 17/20)
To convert from decimal to percentage, multiply by 100.
The efficiency equation can be rearranged to find other quantities:
- Useful energy output = efficiency × total energy input
- Total energy input = useful energy output ÷ efficiency
You must also understand that:
Wasted energy = total energy input - useful energy output
Why no device is 100% efficient
In reality, no device or system can be 100% efficient. There will always be some energy dissipated to the surroundings. Even the most sophisticated machines experience:
- Friction in moving parts (even with lubrication)
- Electrical resistance in conducting materials
- Sound energy from vibrations
- Heat loss through insulation
The only theoretical exception would be a device with no moving parts, perfect insulation, and no electrical resistance — conditions that cannot be achieved in practice.
Some devices have very high efficiency:
- Electric heaters: up to 99% (nearly all electrical energy becomes thermal energy, which is the useful output)
- LED bulbs: 70-90% (far more efficient than traditional filament bulbs at 5%)
- Electric motors: 60-90%
Others are much less efficient:
- Petrol car engines: 20-30% (most energy lost as heat to surroundings)
- Coal power stations: 30-40%
- Traditional filament bulbs: 5% (95% of energy wasted as heat)
Sankey diagrams
Sankey diagrams provide a visual way to represent energy transfers. The width of each arrow is proportional to the amount of energy it represents.
In a Sankey diagram:
- The input energy arrow enters from the left
- The useful energy arrow continues to the right or curves upward
- Wasted energy arrows branch off (usually downward), often labeled as "thermal energy to surroundings"
- The thickness of all output arrows must equal the thickness of the input arrow (conservation of energy)
You may need to draw, interpret or complete Sankey diagrams in your exam. When drawing them:
- Use a ruler for straight lines
- Make arrow widths proportional to the energy values
- Label all arrows with the energy type and value
- Ensure the total width out equals the total width in
Improving efficiency
Understanding how energy is wasted allows us to design more efficient devices. Common strategies include:
Reducing friction:
- Lubrication of moving parts with oil or grease
- Using ball bearings or roller bearings in wheels and axles
- Streamlining shapes to reduce air resistance
- Using magnetic levitation (maglev) to eliminate contact friction
Reducing electrical resistance:
- Using thicker wires (lower resistance)
- Using better conducting materials
- Keeping components cool (resistance increases with temperature)
- Superconductors at very low temperatures (zero resistance)
Reducing thermal energy losses:
- Insulation around hot components or buildings
- Double glazing in windows
- Cavity wall insulation
- Loft insulation
Energy recovery systems:
- Regenerative braking in electric/hybrid vehicles (converts kinetic energy back to electrical energy rather than wasting it as heat)
- Heat exchangers that capture waste heat for useful purposes
Calculations involving efficiency
You must be able to perform calculations using the efficiency equation with energy values (in joules) or power values (in watts).
Remember the key relationships:
For energy:
- Efficiency = useful energy out ÷ total energy in
- Useful energy out = efficiency × total energy in
- Wasted energy = total energy in - useful energy out
For power:
- Efficiency = useful power out ÷ total power in
- Useful power out = efficiency × total power in
- Wasted power = total power in - useful power out
When working with percentages, convert to a decimal first by dividing by 100.
Worked examples
Example 1: Basic efficiency calculation
Question: A motor is supplied with 500 J of electrical energy. It transfers 350 J of energy usefully to kinetic energy. Calculate the efficiency of the motor.
Solution:
Step 1: Identify the values
- Total energy input = 500 J
- Useful energy output = 350 J
Step 2: Select the correct equation
- Efficiency = useful energy transferred ÷ total energy supplied
Step 3: Substitute and calculate
- Efficiency = 350 J ÷ 500 J = 0.70
Step 4: Convert to percentage if required
- Efficiency = 0.70 × 100 = 70%
Answer: 0.70 or 70% [2 marks]
Example 2: Finding wasted energy
Question: An electric motor has an efficiency of 85%. It is supplied with 2400 J of energy. Calculate: a) The useful energy transferred [2 marks] b) The energy wasted [2 marks]
Solution:
Part a: Step 1: Convert efficiency to decimal
- 85% = 0.85
Step 2: Rearrange efficiency equation
- Useful energy = efficiency × total energy input
Step 3: Calculate
- Useful energy = 0.85 × 2400 J = 2040 J
Answer: 2040 J [2 marks: 1 mark for correct rearrangement, 1 mark for answer]
Part b: Step 1: Use the relationship
- Wasted energy = total energy in - useful energy out
Step 2: Calculate
- Wasted energy = 2400 J - 2040 J = 360 J
Answer: 360 J [2 marks: 1 mark for method, 1 mark for answer]
Example 3: Power-based efficiency calculation
Question: A kettle has a useful power output of 1800 W and a total power input of 2000 W. Calculate the efficiency of the kettle and explain what happens to the wasted power. [4 marks]
Solution:
Step 1: Use the power version of the efficiency equation
- Efficiency = useful power output ÷ total power input
Step 2: Substitute values
- Efficiency = 1800 W ÷ 2000 W = 0.90
Step 3: Convert to percentage
- Efficiency = 0.90 × 100 = 90%
Step 4: Explain wasted power
- The wasted power (200 W) is dissipated as thermal energy to the surroundings, heating the kettle casing and the air around it.
Answer: Efficiency = 0.90 or 90%. The remaining 200 W is wasted as thermal energy transferred to the surroundings through the kettle casing and as heat to the air. [4 marks: 2 marks for correct calculation, 2 marks for explanation of energy dissipation]
Common mistakes and how to avoid them
Confusing useful and wasted energy — Always check the question carefully. The useful energy is what the device is designed to produce (e.g., kinetic energy for a motor, light for a bulb). Everything else is wasted.
Forgetting to convert percentages to decimals — When efficiency is given as a percentage, divide by 100 before using it in calculations. For example, 75% becomes 0.75.
Thinking efficiency can exceed 100% — This violates the law of conservation of energy. You cannot get more energy out than you put in. If your answer exceeds 1.0 (or 100%), check your calculation.
Mixing up the efficiency equation — The useful output goes on top, total input on the bottom. Remember: efficiency = out ÷ in (for the useful part).
Not showing working in calculations — In exam questions worth 2+ marks, you must show your working. Write the equation, substitute values, then calculate. You can gain method marks even if your final answer is wrong.
Incorrect units or no units — Efficiency has no units (it's a ratio), but energy must be in joules and power in watts. Always include units for energy and power values but not for efficiency.
Exam technique for "Efficiency of energy transfers"
Command word "Calculate" — You must show your working. Write the equation, substitute the numbers with units, then give your final answer. This is typically worth 2-3 marks.
Command word "Explain" — You need to give reasons why something happens, using scientific knowledge. Link cause and effect. For example, "The motor is inefficient because friction between moving parts transfers kinetic energy to thermal energy in the surroundings."
Rearranging equations — Practice rearranging the efficiency equation to find input energy or useful output when given efficiency. Use the triangle method if it helps: put useful energy at the top, efficiency and total energy at the bottom.
Quality of written communication — Extended response questions (4-6 marks) require clear, logical answers with correct scientific terminology. Use terms like dissipated, thermal energy, and surroundings rather than vague phrases like "lost as heat."
Quick revision summary
Efficiency measures the proportion of input energy that is usefully transferred. Calculate it using: efficiency = useful energy out ÷ total energy in. Efficiency is always less than 1 (or 100%) because energy is dissipated to the surroundings, mainly as thermal energy through friction, air resistance, and electrical resistance. Improve efficiency by reducing friction (lubrication), improving insulation, or using better materials. Sankey diagrams visually represent energy transfers with arrow widths proportional to energy amounts. Always show working in calculations and remember that efficiency has no units.