← Engines and efficiency

Efficiency

An engine takes in 500 J from its fuel. It turns 150 J of that into motion.

What share of the 500 J becomes useful output?

Count it: 150 ÷ 500 = 0.30. The useful output is 0.30 of the input.

That share has a name. The share of the total energy input that a device turns into useful output is called the device's efficiency.

efficiency = useful energy out ÷ total energy in

The engine's efficiency is 0.30.

The engine, workedsteplinevaluesuseful energy out = 150 J, total energy in = 500 Jequationefficiency = useful energy out ÷ total energy insubstituteefficiency = 150 ÷ 500result0.30, or 30%
The engine's share, counted: 150 J of 500 J is 0.30.

Efficiency is often expressed as a percentage: 0.30 × 100 = 30. The engine is 30% efficient.

The percentage reads naturally: 30% efficient means 30 J of every 100 J of input becomes useful output.

Fraction and percentageas a fraction of the inputas a percentage0.3030%0.5555%0.8585%
Multiply the fraction by 100 to speak in percent.

Efficiency is a share, so it has no unit.

The rest of the input is the wasted output: 500 - 150 = 350. 350 J leaves as waste, mostly heat.

energy (J)150 Juseful output350 Jwasted output
The 500 J input split: 150 J useful, 350 J wasted. The useful share is the efficiency, 30%.

Q: A microwave takes in 1200 J and delivers 660 J to the food. Calculate its efficiency, as a percentage.

Write down the values:

useful energy out = 660 J, total energy in = 1200 J, efficiency = ?

Write down the equation:

efficiency = useful energy out ÷ total energy in

Substitute in the values, and calculate:

efficiency = 660 ÷ 1200 = 0.55

As a percentage: 0.55 × 100 = 55

The microwave's efficiency is 55%.

Q: A phone charger takes in 80 J from the outlet and puts 68 J into the battery. Calculate its efficiency, as a percentage.

Write down the values:

useful energy out = 68 J, total energy in = 80 J, efficiency = ?

Write down the equation:

efficiency = useful energy out ÷ total energy in

Substitute in the values, and calculate:

efficiency = 68 ÷ 80 = 0.85

As a percentage: 0.85 × 100 = 85

The charger's efficiency is 85%.

An electric scooter's motor takes in 400 J and delivers 300 J of useful work. Enter its efficiency, as a percentage.

A blender takes in 250 J; 100 J of that becomes the blades' useful work. Lumi says: 'The blender's efficiency is 40%.' Is she correct?

Your turn

A gas water heater takes in 1600 J from burning gas, and 1040 J of that ends up in the water. Enter the heater's efficiency, as a percentage.

A dishwasher is 60% efficient. Which statement says what that means?

An air compressor takes in 900 J of electrical energy; 324 J of that becomes useful work. Enter the compressor's efficiency, as a percentage.

A device turns a share of its total energy input into useful output. What is that share called?