Efficiency (Cambridge (CIE) IGCSE Physics)

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3 October 2024

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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

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

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

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

Calculating efficiency

Extended tier only

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

Efficiency in terms of energy:

$efficiency = \frac{useful energy output}{total energy input} (\times 100 %)$

Efficiency in terms of power:

$efficiency = \frac{useful power output}{total power input} (\times 100 %)$

Worked Example

An electric motor has an efficiency of 35%.

It lifts a 7.2 kg load through a height of 5 m in 3 s.

Calculate the power of the motor.

Answer:

Step 1: Write down the efficiency equation in terms of power

$e fficiency = \frac{useful power output}{total power input} (\times 100 %)$

Step 2: Rearrange to make power input the subject

$power input = \frac{power output}{efficiency \div 100}$ OR $power input = \frac{power output \times 100}{efficiency}$

Step 3: Calculate the power output

$power output = \frac{∆ E}{t}$

$∆ E$ is equal to the change in gravitational potential energy as the load is lifted

$∆ E_{P} = m g ∆ h$

$∆ E_{P} = 7.2 \times 9.8 \times 5$

$∆ E_{P} = 352.8 J$

Therefore:

$power output = \frac{352.8}{3}$

$power output = 117.6 W$

Step 4: Substitute the values into the power input equation

$power input = \frac{117.6}{0.35}$ OR $power input = \frac{117.6 \times 100}{35}$

$power input = 336 W$

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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