# Efficiency Formula

## Efficiency

Efficiency is the ratio of the work performed by a machine or in a process to the total energy expended or heat consumed.

Efficiency refers to how close we can get to a particular outcome of the given input with as much less wastage as possible. Efficiency is the ability to minimise wasting materials, efforts, energy and time in performing something or producing the desired result.

Efficiency can be determined quantitatively by the ratio of useful output to total input. The ratio of energy transferred to a useful form compared to the total energy supplied initially is called the efficiency of the device.

Efficiency is denoted by Î·.

Efficiency formula regarding Work is given as

$$\begin{array}{l}\eta = \frac{\text{Work output}}{\text{Work input}}\times 100\%\end{array}$$

Efficiency formula regarding Energy is given as

$$\begin{array}{l}\eta = \frac{\text{Energy output}}{\text{Energy input}}\times 100\%\end{array}$$

The efficiency formula is applied to calculate the efficiency of any given input. It has no unit and expressed in percentage.

### Solved Examples

Example 1

If a cyclist puts 600 J of work on his bicycle and the bicycle gives out 140 J of useful work. Calculate the efficiency of a cyclist.

Solution:

Given:

Work Input = 600 J,

Work Output = 140 J

The efficiency is given as

Î· ={ Work Output / Work Input }Ã— 100 %

Â  Â = {140 / 600} Ã— 100 %

Â  Â = 23.3 %

Example 2

A heat engine gives out 500 J of heat energy as useful work. Determine the energy supplied to it as input if its efficiency is 40%.

Solution:

Given:

Energy output = 500 J

Efficiency Î· = 40 %

Efficiency Î· = {Energy Output / Energy Input}Ã— 100 %

âˆ´ Energy input = Energy Output / Î·

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  = 500 / 0.40

Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  = 1250 J

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