Efficiency of Machines
Every machine you use — from a bicycle to a car engine — takes in energy and converts it into a more useful form. A bicycle converts chemical energy from your muscles into kinetic energy of motion. However, no machine is perfect: some energy is always lost to unwanted forms, most commonly heat due to friction, or sound. The efficiency of a machine tells us what fraction of the input energy actually ends up doing useful work. It is one of the most important concepts in engineering and everyday physics. Efficiency is expressed as a ratio — useful output energy divided by total input energy. Because output can never exceed input (that would violate conservation of energy), efficiency is always between 0 and 1, or equivalently between 0 % and 100 %. A perfectly efficient machine would have an efficiency of 1 (100 %), meaning every joule put in does useful work. In reality, friction, air resistance, electrical resistance, and other dissipative forces always cause some energy to be wasted, so real machines always fall below 100 %. Understanding efficiency matters far beyond exam questions. Engineers designing electric motors, architects specifying insulation, and governments setting vehicle emissions targets all rely on efficiency calculations. Improving efficiency means getting the same useful output from less input energy, which reduces fuel costs and cuts carbon emissions. Even small percentage improvements across millions of machines add up to enormous real-world impact.
- Input and Output Energy
- Energy Always Dissipates
- Calculating Efficiency
- Efficiency Using Power
- Why 100 % Is Impossible
Input and Output Energy
Every machine receives energy from a source — this is the input energy (E_in). It then converts some of that energy into the desired, useful form — this is the useful output energy (E_out). Think of a kettle: electrical energy goes in, and thermal energy heating the water is the useful output. The steam and heat lost to the air are wasted energy.
Energy Always Dissipates
The First Law of Thermodynamics tells us energy is conserved: E_in = E_useful + E_wasted. Energy cannot be destroyed — it just transforms. Friction converts kinetic energy to heat; electrical resistance converts electrical energy to heat; sound is vibration energy radiated away. These losses are unavoidable in practice, which is why E_out < E_in for every real machine.
Calculating Efficiency
Efficiency (η, the Greek letter eta) is the ratio of useful output energy to input energy. Multiply by 100 to express it as a percentage. For example, if a motor receives 500 J of electrical energy and delivers 350 J of mechanical work, its efficiency is 350 ÷ 500 = 0.70, or 70 %. The remaining 30 % (150 J) was dissipated as heat in the motor's coils and bearings.
Efficiency Using Power
Because power is energy per unit time (P = E/t), and the time is the same for both input and output in a continuously running machine, you can replace energies with powers: η = P_useful / P_input. This is extremely handy when dealing with motors and generators whose ratings are given in watts rather than joules. The formula and its interpretation remain identical.
Why 100 % Is Impossible
The Second Law of Thermodynamics guarantees that some energy will always be degraded to thermal energy during any real energy transfer. Even superconducting electric motors, which eliminate electrical resistance, still have mechanical bearing friction. An efficiency of exactly 100 % would require a perfectly isolated, frictionless system — a theoretical ideal. In practice, large modern power stations achieve about 35–45 %, good electric motors reach 85–95 %, and LED bulbs reach around 40–50 % (compared to ~5 % for incandescent bulbs).
The Key Equation
- \eta — Efficiency (% (dimensionless ratio)): The Greek letter eta; the fraction of input energy converted to useful output, expressed as a percentage.
- E_{\text{useful}} — Useful output energy (Joules (J)): The energy delivered by the machine in the desired form (e.g. mechanical work, light, or thermal energy in the intended object).
- E_{\text{input}} — Input energy (Joules (J)): Total energy supplied to the machine from an external source. Always greater than or equal to useful output energy.
Worked Example
Problem. An electric motor is supplied with 2400 J of electrical energy. It lifts a crate, doing 1560 J of useful mechanical work. (a) Calculate the efficiency of the motor. (b) State how much energy is wasted and describe what form it takes.
Answer. The motor has an efficiency of 65 %. It wastes 840 J, primarily as thermal energy due to electrical resistance and friction.
Origins · 1 minJames Watt and how this was discovered
James Watt dramatically improved the efficiency of the steam engine in the 1760s–70s by adding a separate condenser, nearly tripling the work obtained from the same amount of coal. His systematic analysis of how much useful work an engine could do per unit of fuel consumed laid the practical foundation for the concept of machine efficiency. The SI unit of power, the watt (W), is named in his honour. Watt invented the term 'horsepower' as a marketing tool to convince mine owners his engine could replace their horses — he deliberately set it slightly lower than an actual horse's peak output so his engine would always seem to outperform the competition.
Related Concepts
- Conservation of Energy — Efficiency calculations are built on the principle that total energy is conserved; useful output plus wasted energy must always equal total input energy.
- Work Done by a Force — Useful output energy is often mechanical work done against a load; understanding work (W = Fd cosθ) is essential to quantifying what a machine actually delivers.
- Power — Efficiency can be calculated using power ratings (η = P_useful / P_input) as well as energy values, making power a key related quantity for machines running continuously.
- Energy Losses and Dissipation — The wasted energy in any machine is dissipated — mainly as heat through friction and resistance — which is why understanding energy dissipation is inseparable from efficiency.