Efficiency (Cambridge International IGCSE Physics)

Efficiency of energy transfer

Spec point — 1.7.7 · Understand, qualitatively, the concept of 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

  • If a lamp is 25% efficient, this means that 25% of the energy supplied to it is transferred usefully as light, and the other 75% is wasted.

• No system reaches 100% efficiency

  • Energy is always wasted into other non-useful forms, such as sound and thermal energy which is lost to the surroundings (often due to friction)

Calculating efficiency

Spec point — 1.7.7 · Define efficiency as: (a) (%) efficiency = (useful energy output)/(total energy input) (× 100%) (b) (%) efficiency = (useful power output)/(total power input) (× 100%) recall and use these equations

Calculating efficiency

Extended Tier Only

• Efficiency can be calculated using two equations

• Efficiency in terms of energy:

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

• Efficiency in terms of power:

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

• Efficiency can be given as a decimal between 0 and 1, or as a percentage between 0 and 100%.

• 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 about 70% of the energy from the fuel is wasted inside the power station, mostly as thermal energy transferred to the surroundings, and only about 30% is transferred usefully as electrical energy

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.

[4]

Answer:

Step 1: List the known quantities

• Mass of load, $m$ = 7.2 kg
• Change in height, $h$ = 5.0 m
• Gravitational field strength, $g$ = 9.8 N/kg
• Time, $t$ = 3 s
• Efficiency = 35% or 0.35

Step 2: Calculate the power output of the motor

• The useful energy output is the work done in lifting the load
• The useful power output is that energy divided by the time taken

$\mathrm{power} \mathrm{output}=\frac{\Delta E}{t}$

• $\Delta E$ is equal to the change in gravitational potential energy as the load is lifted

$\Delta E_{P}=mg\Delta h$

$\Delta E_{P}=7.2\times9.8\times5.0=352.8J$ [1 mark]

• Therefore:

$\mathrm{power} \mathrm{output}=\frac{352.8}{3}=117.6W$ [1 mark]

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

$\mathrm{efficiency}=\frac{\mathrm{useful} \mathrm{power} \mathrm{output}}{\mathrm{total} \mathrm{power} \mathrm{input}}$

Step 4: Rearrange to make power input the subject

$\mathrm{power} \mathrm{input}=\frac{\mathrm{power} \mathrm{output}}{\mathrm{efficiency}}$

Step 5: Substitute the values into the power input equation

$\mathrm{power} \mathrm{input}=\frac{117.6}{0.35}$ [1 mark]

$\mathrm{power} \mathrm{input}=336W$ [1 mark]

Exam Hint Efficiency can be given in a decimal (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 decimal = 0.25, percentage = 0.25 × 100 = 25%

Remember that efficiency is calculated using the useful energy or power output. Efficiency has no units, and can never exceed 100%.

Efficiency video

Spec point — 1.7.7 · nan