Efficiency

Machines and devices transfer energy from one store to another. Not all the input energy becomes useful output; some is wasted, often as heat or sound. Efficiency tells us how good a device is at turning input energy (or power) into useful output.

Definition and Equations

Efficiency compares useful output with total input. It can be calculated using energy or power:

$$\text{Efficiency (\%)} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\%$$

$$\text{Efficiency (\%)} = \frac{\text{useful power output}}{\text{total power input}} \times 100\%$$

Efficiency has no unit. We often give it as a percentage. Values are between 0% and 100%.

Useful vs Wasted Energy

• Useful: the form of energy you want (e.g. light from a lamp, kinetic energy from a motor).
• Wasted: energy spread out so it cannot do useful work (e.g. heating due to friction, sound).

Energy is conserved: input = useful output + wasted energy.

Improving Efficiency

• Reduce friction using lubrication or smoother parts.
• Insulate to reduce heat losses (e.g. in kettles or houses).
• Streamline shapes to reduce air resistance.
• Use materials with low electrical resistance to reduce heating in wires.

Sankey Diagrams

A Sankey diagram shows energy in and out with arrows. The arrow width shows the amount of energy. The main forward arrow is useful output; side arrows show wasted energy (often heat).

Common Misconceptions

• Efficiency cannot be above 100%.
• High power does not always mean high efficiency.
• Percent (%) is not a unit; efficiency is a ratio expressed as a percentage or decimal.