P2: Conservation and Efficiency
Understand the conservation of energy principle, calculate efficiency, and learn how to reduce wasted energy and improve the efficiency of devices.
Conservation of Energy
The Principle of Conservation of Energy
Energy cannot be created or destroyed. It can only be transferred from one store to another. This is one of the most fundamental principles in physics and applies to all energy transfers in all situations.
This means that the total energy input to a system must always equal the total energy output. However, not all of the output energy will be in useful stores. Some will be dissipated (wasted) to the surroundings.
Total Energy = Useful Energy + Wasted Energy
In any real system, some energy is always transferred to unwanted stores. This does not violate conservation of energy because the wasted energy still exists, it is just in a form that is not useful for the intended purpose.
Worked Example: Conservation in a Light Bulb
An old-style filament light bulb receives 100 J of electrical energy each second. It transfers 5 J to light energy and 95 J to thermal energy (heat). The total energy output is 5 + 95 = 100 J, which equals the total energy input. Energy is conserved.
What is Useful and Wasted Energy?
Useful energy is the energy transferred to the store that the device is designed for. Wasted energy is energy transferred to stores that are not the intended purpose of the device. For example, a kettle is designed to heat water, so thermal energy is useful. But for an electric motor, thermal energy from friction is wasted because the motor is designed to produce kinetic energy.
Efficiency
Efficiency tells us what fraction of the total energy input is usefully transferred. The higher the efficiency, the less energy is wasted.
Efficiency Equation
Efficiency = useful output energy / total input energy × 100%
Efficiency = (useful energy out / total energy in) × 100%
You can also calculate efficiency using power:
Efficiency = useful output power / total input power × 100%
Understanding Efficiency Values
Efficiency is always a value between 0% and 100%. No device can be more than 100% efficient because energy cannot be created. A device that is 100% efficient would transfer all input energy to useful output with zero wasted energy, which is impossible in practice due to dissipation.
Worked Example 1
A lamp transfers 40 J of light energy for every 200 J of electrical energy supplied. Calculate the efficiency.
Efficiency = (useful output / total input) × 100%
Efficiency = (40 / 200) × 100%
Efficiency = 0.2 × 100%
Efficiency = 20%
Worked Example 2
An electric motor has a power input of 800 W. It transfers 600 W of useful power to a machine. Calculate the efficiency.
Efficiency = (useful output power / total input power) × 100%
Efficiency = (600 / 800) × 100%
Efficiency = 0.75 × 100%
Efficiency = 75%
Worked Example 3
A TV has an efficiency of 35%. It is supplied with 1200 J of electrical energy. Calculate the useful energy output.
Efficiency = useful output / total input × 100%
35% = useful output / 1200 × 100%
0.35 = useful output / 1200
Useful output = 0.35 × 1200
Useful output = 420 J
Worked Example 4
A machine has an efficiency of 60%. It needs to deliver 900 J of useful output energy. Calculate the total energy input required.
Efficiency = useful output / total input × 100%
60% = 900 / total input × 100%
0.60 = 900 / total input
Total input = 900 / 0.60
Total input = 1500 J
Worked Example 5
A washing machine uses 2.5 kW of electrical power. It transfers 1.75 kW as useful power. Calculate the efficiency and the power wasted.
Efficiency = (1.75 / 2.5) × 100% = 0.7 × 100% = 70%
Wasted power = total input - useful output = 2.5 - 1.75 = 0.75 kW = 750 W
Useful and Wasted Energy in Common Devices
| Device | Useful Energy Output | Wasted Energy Output |
|---|---|---|
| Electric heater | Thermal (heat) | Light (small amount) |
| Electric kettle | Thermal (heat water) | Sound, thermal (to surroundings) |
| Electric motor | Kinetic (movement) | Thermal (friction), sound |
| Light bulb (LED) | Light | Thermal (small amount) |
| Light bulb (filament) | Light | Thermal (very large amount) |
| Loudspeaker | Sound (kinetic of air) | Thermal, kinetic (vibration) |
| Car engine | Kinetic (movement) | Thermal, sound |
The useful output depends on the purpose of the device. A heater produces thermal energy as useful output, but for a motor the thermal energy from friction is wasted. Always consider what the device is designed to do before deciding which energy is useful and which is wasted.
Improving Efficiency
Improving efficiency means reducing the amount of wasted energy. There are several ways to do this depending on the device.
Reducing Friction
In moving parts, friction causes energy to be dissipated as thermal energy. Lubricating moving parts with oil or grease reduces friction and therefore reduces wasted thermal energy. This improves the efficiency of engines, motors, and machines with moving parts.
Reducing Air Resistance
Streamlining the shape of vehicles reduces air resistance, which means less energy is wasted as thermal energy. This is why racing cars and aeroplanes have streamlined shapes. Cyclists also adopt aerodynamic positions to reduce air resistance.
Reducing Electrical Resistance
In electrical circuits, resistance in wires causes energy to be dissipated as thermal energy. Using thicker wires reduces resistance. Using superconductors (materials with zero resistance at very low temperatures) eliminates energy loss from resistance entirely, but these are expensive and impractical for most uses.
Using Better Insulation
In heating systems, thermal energy can escape to the surroundings through walls, pipes, and roofs. Using better insulation (such as cavity wall insulation, loft insulation, and lagging on hot water pipes) reduces the rate of thermal energy transfer to the surroundings, meaning less energy is wasted and the system is more efficient.
Using More Efficient Technologies
Replacing old technologies with more efficient ones makes a big difference. For example, LED light bulbs are much more efficient than filament bulbs because they produce much less wasted thermal energy. An LED bulb might be 80% efficient compared to a filament bulb at only 5% efficient.
Worked Example: Comparing Bulb Efficiencies
A filament bulb and an LED bulb each need to produce 400 J of light energy.
The filament bulb is 5% efficient:
Total input = 400 / 0.05 = 8000 J
Wasted energy = 8000 - 400 = 7600 J
The LED bulb is 80% efficient:
Total input = 400 / 0.80 = 500 J
Wasted energy = 500 - 400 = 100 J
The LED bulb uses far less electrical energy and wastes far less energy as heat.
Efficiency and Sankey Diagrams
Sankey diagrams can be used to represent efficiency visually. A more efficient device will have a larger proportion of the arrow going straight ahead (useful energy) and a smaller proportion turning off (wasted energy).
Drawing Efficiency on Sankey Diagrams
The input arrow represents the total energy. It splits into useful output (going straight) and wasted output (going to the side or down). The relative widths of the arrows directly show the efficiency. For a 75% efficient device, the useful arrow is three times wider than the wasted arrow.
Worked Example: Sankey Diagram and Efficiency
A motor has 1000 J of energy input. It is 70% efficient.
Useful output = 70% of 1000 = 700 J
Wasted output = 30% of 1000 = 300 J
The Sankey diagram input arrow would be drawn with a width proportional to 1000 J. It splits into a useful output arrow 70% of that width going straight ahead, and a wasted output arrow 30% of that width turning downwards.
Practice Questions
1. A device uses 500 J of energy and transfers 350 J usefully. Calculate the efficiency.
Efficiency = (350 / 500) × 100% = 0.7 × 100% = 70%
2. An electric motor has an efficiency of 80%. It is supplied with 2500 J of electrical energy. Calculate the useful energy output and the wasted energy.
Useful output = 0.80 × 2500 = 2000 J. Wasted energy = 2500 - 2000 = 500 J
3. A machine is 40% efficient and needs to deliver 600 J of useful output. Calculate the total energy input required.
Total input = 600 / 0.40 = 1500 J
4. State the principle of conservation of energy.
Energy cannot be created or destroyed. It can only be transferred from one store to another.
5. Explain how lubricating the moving parts of a machine improves its efficiency.
Lubrication reduces friction between moving parts. Less friction means less energy is dissipated as thermal energy to the surroundings, so more of the input energy is transferred usefully and the efficiency increases.
6. An LED bulb is 85% efficient and produces 680 J of light energy. Calculate the total electrical energy input and the energy wasted as heat.
Total input = 680 / 0.85 = 800 J. Wasted energy = 800 - 680 = 120 J
🔢 Maths Skills
Mathematical Skills for this Topic
Rearranging the efficiency formula: The efficiency equation can be written in three ways depending on what you need to find. Efficiency = useful output / total input (gives a decimal). To find useful output: useful output = efficiency × total input. To find total input: total input = useful output / efficiency. Always convert a percentage efficiency to a decimal before using it in calculations (e.g. 65% = 0.65).
Expressing efficiency as a decimal and percentage: A decimal efficiency of 0.35 is the same as 35%. To convert from decimal to percentage, multiply by 100. To convert from percentage to decimal, divide by 100. Efficiency can never be greater than 1 (or 100%) because energy cannot be created. An efficiency of 0 means all energy is wasted; an efficiency of 1 means no energy is wasted (impossible in practice).
Calculating wasted energy: Once you know the efficiency and total input, wasted energy = total input − useful output. Alternatively, wasted energy = total input × (1 − efficiency as a decimal). For example, if a device is 70% efficient with 1000 J input, wasted energy = 1000 × (1 − 0.70) = 1000 × 0.30 = 300 J.
Percentage change in efficiency: If an old bulb is 5% efficient and a new one is 80% efficient, the percentage improvement is NOT simply 80 − 5 = 75%. Percentage improvement = ((80 − 5) / 5) × 100% = 1500% improvement. However, you can say the new bulb is 75 percentage points more efficient.
⚠️ Common Misconceptions
Watch Out!
Students often think that "efficient" means no energy is wasted at all. Wrong: An efficient device wastes no energy — all the input energy becomes useful output. Correct: No device can be 100% efficient. Even the most efficient machines always waste some energy, usually as thermal energy due to friction or electrical resistance. An efficient device simply wastes less energy than an inefficient one.
Students often think that wasted energy disappears. Wrong: Wasted energy disappears and no longer exists in the system. Correct: Wasted energy is transferred to the thermal energy store of the surroundings. It still exists — it is just no longer in a useful form. The total energy is always conserved: useful output + wasted output = total input.
✍️ 6-Mark Question
Extended Answer Question
6 marks: Explain why a car engine can never be 100% efficient and discuss ways to improve its efficiency.
A car engine can never be 100% efficient because energy is always dissipated to unwanted stores. Friction between the moving parts of the engine (pistons, gears, crankshaft) transfers some energy to the thermal energy store of the engine components and the surrounding air. Hot exhaust gases carry thermal energy away from the engine, which is wasted. Sound energy from the engine and exhaust is also a form of dissipation. Air resistance on the moving parts wastes further energy. These energy losses are unavoidable because friction and heating are inherent to any mechanical process involving motion and combustion.
There are several ways to improve efficiency. Lubricating moving parts with oil reduces friction, so less energy is transferred to thermal stores. Streamlining the car body reduces air resistance, so less energy is needed to maintain speed. Using materials with lower thermal conductivity for the engine block can reduce heat loss. Hybrid engines that recover kinetic energy during braking (regenerative braking) and reuse it improve overall efficiency. Ensuring tyres are properly inflated reduces rolling resistance. Regular maintenance keeps the engine running at its optimal efficiency.
Mark scheme: 2 marks for explaining why 100% efficiency is impossible (friction, thermal losses), 2 marks for describing specific methods to improve efficiency (lubrication, streamlining, regenerative braking), 1 mark for explaining how each method reduces wasted energy, 1 mark for a concluding statement about the limit of efficiency
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
A factory needs to choose between two electric motors to drive a conveyor belt. Both deliver the same useful output power of 4.5 kW.
| Motor | Input Power | Cost | Running Hours per Year |
|---|---|---|---|
| Motor A | 6.0 kW | £200 | 4000 h |
| Motor B | 5.0 kW | £500 | 4000 h |
Electricity costs 25p per kWh. Calculate which motor is more cost-effective over 2 years, taking into account both purchase cost and running cost.
Answer: Motor A wasted power = 6.0 − 4.5 = 1.5 kW. Running cost A = 6.0 × 4000 × 0.25 = £6000 per year. Over 2 years = £12 000. Total A = £200 + £12 000 = £12 200.
Motor B wasted power = 5.0 − 4.5 = 0.5 kW. Running cost B = 5.0 × 4000 × 0.25 = £5000 per year. Over 2 years = £10 000. Total B = £500 + £10 000 = £10 500.
Motor B is more cost-effective by £12 200 − £10 500 = £1700 over 2 years, despite costing £300 more to buy. The higher efficiency saves more in electricity costs than the additional purchase price.
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