## Efficiency Formula

It is used to make sure that a machine is to be employed for a particular purpose or not by measuring its efficiency.

## Definition

Efficiency, in any given system, is the ratio of the output of the energy to the input of the energy. In other words, it is the ratio of the work done by the machine to the total heat consumed by the machine. The resulting ratio is then converted into percentage. So, efficiency is expressed in a percentage form.

It is basically used to calculate how a particular output for a given input can be achieved so that the least amount of wastage of energy, material, effort and time occurs in the whole process.

Efficiency is denoted by Ƞ. It has no units.

## Formula

**For work:**

Ƞ = (Work Output/Work Input) × 100

**For Energy:**

Ƞ = (Energy Output/Energy Input) × 100

## Solved Examples

To better understand the topic, below are some examples to help you out.

**Ex. 1. A heat energy of 600 J is produced as work done by a heat engine. If the efficiency of the engine is 30% then find the input energy supplied.**

**Solution: **

Given: Energy output = 600J

Efficiency = 30%

Ƞ = (Energy Output/Energy Input) × 100

So, Energy Input = (Energy Output/ Ƞ) * 100

= 600/0.30

= 2000 J

**Ex. 2. A cyclist on his bicycle puts 400J of work and the useful work given out is 100J, then what is the efficiency of the cyclist?**

**Solution: **

Given:

Work Output = 400 J

Work Input = 100 J

Efficiency = ?

Ƞ = (Work Output/Work Input) × 100

Ƞ = (100/400) × 100

Ƞ = 25%

**Ex. 3. A specific process has an efficiency of just 5.00%. To finish this huge process, 150,000 J of energy is supplied. What is the energy output produced?**

**Solution: **

Given: Efficiency = 5.00%

Energy Input = 150000 J

Energy Output = ?

Ƞ = (Energy Output/Energy Input) × 100

Energy Output= Energy Input × Ƞ/100

= 150000 × 5/100

= 7500 J

Hence, the energy output produced is 7500 J.