Efficiency Formula

The efficiency of an object is defined as the ability to get close to a certain output from a given input with the least amount of waste. It can be interpreted as the amount of labor or energy saved in a process. Mathematically, it is the ratio of work accomplished by a machine or process to total energy expanded or heat consumed.  It is denoted by the symbol eta (η). Its formula equals the ratio of output work to input work multiplied by 100. Its unit of measurement is a percentage (%).

Efficiency Formula

η = (W_o/W_i) × 100

Where,

• η is the percentage efficiency,
• W_o is the output work,
• W_i is the input work.

In terms of input energy and output energy, the formula is given as,

η = (E_o/E_i) × 100

Where,

• η is the percentage efficiency,
• E_o is the output work,
• E_i is the input work.

Sample Problems

Problem 1: Calculate the efficiency of a machine if input energy is 200 J and output energy is 150 J.

Solution:

We have,

E_o = 150

E_i = 200

Using the formula we have,

η = (E_o/E_i) × 100

= (150/200) × 100

= 75%

Problem 2: Calculate the efficiency of a machine if input energy is 450 J and output energy is 300 J.

Solution:

We have,

E_o = 300

E_i = 450

Using the formula we have,

η = (E_o/E_i) × 100

= (300/450) × 100

= 66.67%

Problem 3: Calculate the efficiency of a motor engine if 500 J work is done to give an output work of 100 J.

Solution:

We have,

W_o = 100

W_i = 500

Using the formula we have,

η = (W_o/W_i) × 100

= (100/500) × 100

= 20%

Problem 4: Calculate the output energy if the efficiency of a machine is 52% and the input energy is 250 J.

Solution:

We have,

η = 52%

E_i = 250

Using the formula we have,

η = (E_o/E_i) × 100

=> E_o = nE_i/100

= 52 (250)/100

= 130 J

Problem 5: Calculate the output energy if the efficiency of a machine is 72% and the input energy is 420 J.

Solution:

We have,

η = 72%

E_i = 420

Using the formula we have,

η = (E_o/E_i) × 100

=> E_o = nE_i/100

= 72 (420)/100

= 302.4 J

Problem 6: Calculate the input energy if the efficiency of a machine is 45% and the output energy is 300 J.

Solution:

We have,

η = 45%

E_o = 300

Using the formula we have,

η = (E_o/E_i) × 100

=> E_i = (E_o/n) × 100

= (300/45) × 100

= 666.67 J

Problem 7: Calculate the input energy if the efficiency of a machine is 56% and the output energy is 600 J.

Solution:

We have,

η = 56%

E_o = 600

Using the formula we have,

η = (E_o/E_i) × 100

=> E_i = (E_o/n) × 100

= (600/56) × 100

= 1071.42 J

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