Physical ScienceEnergy, Work and HeatHS-PS3-3

Efficiency

Efficiency is useful energy out divided by energy in, and it is always less than 100%.

Not started Jump to practice

No machine turns all of the energy you put in (by doing work on it, or by plugging it in) into the form you want. A car engine, a light bulb and your own muscles all let some energy escape, mostly as heat. By conservation of energy, none of it vanishes; it just isn't useful. Efficiency is the useful share, as a percent.

Key idea

$$\text{efficiency} = \dfrac{\text{useful energy out}}{\text{energy in}} \times 100\%$$ It is always less than 100%, because some energy always leaves as heat, sound or other forms you didn't want.

Why it works

Energy in = useful energy out + wasted energy. Since the wasted part is never zero in a real machine (there is always some friction, resistance or heat loss), the useful part is always smaller than the input. A machine that put out more energy than it took in would be creating energy, which never happens.
A block sliding down a ramp with friction. Some of the potential energy becomes kinetic energy and some becomes thermal energy (red-orange). The total stays the same, but only part of it is motion.

Worked example: A motor

An electric motor takes in 500 J and lifts a load, giving it 400 J of potential energy. Find its efficiency.
  1. $\text{efficiency} = \dfrac{400}{500} \times 100\% = 80\%$.
  2. The other 100 J became heat and sound.

Answer: 80%

Worked example: Useful output

A lamp is 25% efficient and uses 2,000 J. How much light energy does it give?
  1. 25% of 2,000 J: $0.25 \times 2{,}000 = 500$ J of light.
  2. The other 1,500 J heats the lamp and the room.

Answer: 500 J

Common mistake

Believing a well-built machine can put out more energy than it takes in. Better design can only cut the waste; it can't make energy. Check: if you get an efficiency over 100%, you have swapped "in" and "out."
Most gasoline car engines turn less than a third of their fuel's energy into motion; the rest leaves as heat through the radiator and the exhaust.

Practice

Pass with 3 right answers, the last 2 in a row. Each right answer earns 1 XP.

Loading practice…

Builds on

Leads to

Sources and further reading

  • OpenStax, College Physics 2e, 7.6 Conservation of Energy
  • OpenStax, College Physics 2e, 15.5 Applications of Thermodynamics: Heat Engines
  • Next Generation Science Standards, HS-PS3-3
@teddyrookbook GitHub