Every device that transfers energy wastes some of it — usually as heat or sound. Efficiency measures how well a device converts input energy into useful output. No real device reaches 100% efficiency, but understanding the losses helps engineers design better ones.
What is efficiency?
Efficiency is the fraction (or percentage) of the total energy input that is transferred usefully by a device. It has no units because it is a ratio of two energies.
Efficiency formula:
Efficiency = useful energy output ÷ total energy input
Or, as a percentage:
Efficiency (%) = (useful energy output ÷ total energy input) × 100
The efficiency value is always between 0 and 1 (or 0% and 100%). An efficiency of 0.80 means 80% of input energy is usefully transferred; the remaining 20% is wasted (usually as heat or sound).
An alternative form using power:
Efficiency = useful power output ÷ total power input
This version is useful when the question gives power (in watts) rather than energy (in joules).
How do you calculate efficiency — worked examples?
Example 1: A light bulb has a total input power of 60 W and produces 9 W of useful light energy. Calculate its efficiency.
- Efficiency = useful power output ÷ total power input
- Efficiency = 9 ÷ 60
- Efficiency = 0.15 (or 15%)
- Wasted power = 60 − 9 = 51 W (mostly heat)
Example 2: A motor receives 500 J of electrical energy and does 350 J of useful mechanical work. Calculate its efficiency.
- Efficiency = 350 ÷ 500
- Efficiency = 0.70 (or 70%)
- Wasted energy = 500 − 350 = 150 J (heat from friction in the motor)
Example 3 (rearranging): A pump has an efficiency of 0.65. It receives 800 J of electrical energy. How much useful work does it do?
- Useful energy output = efficiency × total energy input
- Useful output = 0.65 × 800
- Useful output = 520 J
- Wasted energy = 800 − 520 = 280 J
What is a Sankey diagram?
A Sankey diagram is a flow diagram that shows the transfer and transformation of energy through a device. It makes efficiency visible at a glance:
- The arrow flows from left to right, representing energy moving through the device.
- The width of the arrow is proportional to the amount of energy it represents — a wider arrow means more energy.
- Useful energy is shown going straight on (or upward) from the device.
- Wasted energy (usually heat or sound) is shown branching downward from the device.
- The total width of all output arrows equals the total width of the input arrow, because energy is conserved.
Reading a Sankey diagram: If the main (useful) output arrow is nearly as wide as the input arrow, the device is efficient. If most of the width bends downward as waste heat, the device is inefficient.
Constructing a Sankey diagram step by step:
For a coal-fired power station that converts 1,000 J of chemical energy from coal:
- 350 J → useful electrical energy output
- 400 J → wasted as heat in steam/cooling towers
- 150 J → wasted as heat in generators
- 100 J → wasted as heat and noise in transmission
- Draw the input arrow on the left, width proportional to 1,000 J.
- The output section splits:
- An arrow going straight (width proportional to 350 J) labelled "electrical energy"
- An arrow bending down (400 J) labelled "heat — cooling towers"
- An arrow bending down (150 J) labelled "heat — generators"
- An arrow bending down (100 J) labelled "heat + noise — transmission"
- Check: 350 + 400 + 150 + 100 = 1,000 J ✓
Efficiency = 350 ÷ 1,000 = 0.35 (35%)
What are the efficiencies of common devices?
| Device | Approximate efficiency | Main type of wasted energy |
|---|---|---|
| LED light bulb | ~90% | Heat |
| Traditional filament bulb | ~5% | Heat (mostly infrared) |
| Electric motor | ~85–95% | Heat (friction, resistance) |
| Petrol engine (car) | ~25–30% | Heat from combustion |
| Solar panel | ~15–22% | Reflected light; heat |
| Coal power station | ~33–38% | Heat in cooling towers |
| Combined-cycle gas turbine | ~55–60% | Heat |
LED bulbs replaced filament bulbs largely because of the dramatic difference in efficiency: a 10 W LED produces the same light output as a 60 W filament bulb. The filament bulb wastes 50 W as heat.
How can efficiency be improved?
Wasted energy usually leaves as heat (due to friction or electrical resistance) or sound. Engineers improve efficiency by:
| Method | How it reduces waste |
|---|---|
| Lubrication (oil, grease) | Reduces friction between moving parts → less heat generated |
| Streamlining (aerodynamic design) | Reduces air resistance → less kinetic energy lost to heat in the air |
| Thermal insulation | Reduces heat lost from engines, boilers, buildings |
| Electrical resistance reduction | Thicker or superconducting cables reduce I²R losses |
| Regenerative braking (electric vehicles) | Converts braking kinetic energy back into electrical energy (rather than wasting it as heat in brake pads) |
Frequently asked questions
What does an efficiency of 0.75 mean in practice?
An efficiency of 0.75 (75%) means that for every 100 J of energy put into the device, 75 J is transferred usefully and 25 J is wasted — usually as heat. It does not mean the device "loses" energy in the sense that energy disappears; energy is always conserved. It means 25% of the input energy ends up in a form that is not useful for the intended purpose, typically dispersed as heat into the surroundings where it cannot easily be recovered.
Why can no device have an efficiency greater than 100%?
Because energy cannot be created — only transferred or transformed. The law of conservation of energy states that the total energy output of any device must equal the total energy input. A device cannot produce more useful energy than the energy supplied to it. If a calculation gives an efficiency greater than 1 (or 100%), there is an error — check whether useful output and total input values have been swapped.
What is the difference between efficiency and power?
Power is the rate at which energy is transferred — how quickly a device does work, measured in watts (W = J/s). Efficiency is the ratio of useful output to total input — it tells you what fraction of energy is transferred usefully, regardless of how fast. A powerful device can still be inefficient (a jet engine is very powerful but wastes a lot of energy as heat), and a weak device can be highly efficient (a small LED is low power but converts most input to light).
Why do Sankey arrows always have to have the same total width on the output side as the input side?
Because energy is conserved — it cannot be created or destroyed, only transferred or transformed. The total output energy (useful + wasted) must equal the total input energy. In a Sankey diagram, arrow width represents amount of energy, so the combined width of all output arrows must equal the width of the input arrow. If they did not, the diagram would imply that energy was being created or destroyed, which would violate the first law of thermodynamics.
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