IGCSEPhysicsCambridge (CIE)Revision Notes1. Motion, Forces & EnergyEnergy, Work & PowerEfficiency

Efficiency (Cambridge (CIE) IGCSE Physics): Revision Note

Exam code: 0625 & 0972

Last updated

Efficiency of energy transfer

  • The efficiency of a system is a measure of the amount of useful and wasted energy in an energy transfer

  • Efficiency is defined as:

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

Calculating efficiency

Extended tier only

  • Efficiency is represented as a percentage and can be calculated using two equations

  • Efficiency in terms of energy:

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

  • Efficiency in terms of power:

efficiency space equals space fraction numerator useful space power space output over denominator total space power space input end fraction space open parentheses cross times 100 percent sign close parentheses

  • In the production of electricity:

    • Energy is used to heat water to produce steam

    • The steam turns a turbine

    • The turbine turns a generator

    • The generator produces electricity 

      • At each stage of this process, energy is dissipated to the surroundings

  • The overall efficiency of a typical thermal power station is approximately 30%

    • This means that 70% of the energy transferred from the power station to the National Grid is wasted energy

Sankey diagram of electricity production

cie-1-8-6-sankey-diagram-of-power-station-efficiency

Sankey diagram showing the energy transfers involved in generating electricity in a gas-fired power station

Worked Example

An electric motor lifts a 7.2 kg load through a height of 5.0 m in 3 seconds. The efficiency of the motor is 35%.

Calculate the power supplied to the motor.

Answer:

Step 1: List the known quantities

  • Mass of load, m = 7.2 kg

  • Change in height, h = 5.0 m

  • Acceleration of free fall, g = 9.8 m/s2

  • Time, t = 3 s

  • Efficiency = 35% or 0.35

Step 2: Calculate the power output of the motor

  • The power supplied by the motor is the work done, or energy transferred, to lift the load

power space output space equals space fraction numerator increment E over denominator t end fraction

  • increment E is equal to the change in gravitational potential energy as the load is lifted

increment E subscript P space equals space m g increment h

increment E subscript P space equals space 7.2 cross times 9.8 cross times 5.0 space equals space 352.8 space straight J

  • Therefore:

power space output space equals space fraction numerator 352.8 over denominator 3 end fraction space equals space 117.6 space straight W

Step 3: Write down the efficiency equation in terms of power

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

Step 4: Rearrange to make power input the subject

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

Step 5: Substitute the values into the power input equation 

power space input space equals space fraction numerator 117.6 over denominator 0.35 end fraction

power space input space equals space 336 space straight W

Examiner Tips and Tricks

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

If the question asks for efficiency as a ratio, give your answer as a fraction or decimal.

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

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

Remember that efficiency has no units

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