GCSEPhysics: Combined ScienceOCR GatewayRevision Notes7. Energy7.2 Power & Efficiency7.2.4 Efficiency

Efficiency (OCR Gateway GCSE Physics: Combined Science)

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Efficiency

  • The efficiency of a system is a measure of the amount of wasted energy in an energy transfer
  • Efficiency is defined as:

The ratio of the useful energy output from a system to its total energy input

  • If a system has high efficiency, this means most of the energy transferred is useful
  • If a system has low efficiency, this means most of the energy transferred is wasted
  • Efficiency can be represented as a decimal or as a percentage
  • The equations for efficiency are: 

efficiency space equals space fraction numerator useful space output space energy space transfer over denominator total space input space energy space transfer end fraction

 

efficiency space equals fraction numerator space useful space power space output over denominator total space power space input end fraction

  • Since power is the energy transferred per unit time, power can also be used to calculate efficiency

Worked example

The blades of a fan are turned by an electric motor. In one second, 300 J of energy is transferred electrically from the mains supply. 85 J is wasted due to friction and sound.

Calculate the percentage efficiency of the motor.

Answer: 

Step 1: List the known quantities

  • Total energy input = 300 J
  • Total wasted energy = 85 J

Step 2: State the equation

efficiency space equals fraction numerator space useful space energy space output over denominator total space energy space output end fraction space cross times space 100 percent sign

Step 3: Determine total energy output

  • Due to the conservation of energy:

total energy input = total energy output

  • Therefore, total energy output = 300 J

 

Step 4: Calculate the useful energy output

  • Due to the conservation of energy:

Total energy output = useful energy output + wasted energy

Useful energy output = total energy output − wasted energy

Useful energy output = 300 − 85 

Useful energy output = 215 J

Step 5: Substitute these values into the efficiency equation 

efficiency space equals fraction numerator space useful space energy space output over denominator total space energy space output end fraction space cross times space 100 percent sign

efficiency space equals fraction numerator space 215 space over denominator 300 end fraction space cross times space 100 percent sign

efficiency space equals space 72 percent sign

Exam Tip

Efficiency can be given in a ratio (between 0 and 1) or percentage format (between 0 and 100 %)

If the answer is required as a percentage, remember to multiply the ratio by 100 to convert it:

  • if the ratio = 0.25
  • the percentage = 0.25 × 100 = 25 %

Remember that efficiency has no units

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    Leander

    Author: Leander

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.