Study Guides/Physics/Efficiency Formula in Physics
Study Guide · Physics

Efficiency Formula in Physics

In the study of 'Work, Energy, and Power', scientists and engineers design machines (like car engines, electric motors, or even simple pulleys) to make work easier. However, no machine is perfect. To measure how good a machine is at its job, we calculate its 'Efficiency'.

Question (Click to Flip)

Can efficiency be greater than 100%?

Answer

No. According to the Law of Conservation of Energy, you cannot create energy out of nothing. A machine cannot give out more energy than you put into it.

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Key Facts

An 'Ideal Machine' is a theoretical, imaginary machine that has no friction and is 100% efficient. It does not exist in reality.

LED bulbs are highly efficient because they convert almost all electrical input into Light output, whereas old incandescent bulbs wasted 90% of their energy generating useless Heat.

1. What is Efficiency?

Efficiency (usually denoted by the Greek lowercase letter eta, $\eta$) is defined as the ratio of the useful energy output produced by a machine to the total energy input given to the machine.

  • It tells us how much of our fuel/electricity was actually used to do the job, and how much was completely wasted.

2. The Main Formula

The standard mathematical formula is: Efficiency ($\eta$) = $\frac{\text{Useful Work Output}}{\text{Total Work Input}}$

  • Because both output and input are measured in Joules (J), they cancel each other out. Therefore, efficiency has no unit.

3. Percentage Formula

In real-life engineering, efficiency is almost always expressed as a percentage (%). To get this, simply multiply the result by 100.

Efficiency (%) = $\left( \frac{\text{Power Output}}{\text{Power Input}} \right) \times 100$

4. Why is Efficiency never 100%?

If you put 100 Joules of energy (petrol) into a car, you will never get 100 Joules of forward movement out of it.

  • A massive chunk of that energy is wasted in overcoming Friction between the engine parts.
  • The energy is lost to the environment in the form of Heat and Sound (the noise of the engine).
  • Most petrol car engines have a terrible efficiency of only 20% to 30%!

Questions and Answers

Can efficiency be greater than 100%?+

No. According to the Law of Conservation of Energy, you cannot create energy out of nothing. A machine cannot give out more energy than you put into it.

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