IB Physics SL A.3.13 Efficiency Question Bank

Practise calculating efficiency from useful output, input power, Sankey diagrams and real energy systems in exam questions.

Exam points

Calculate efficiency as useful output divided by total input using power, energy and Sankey data.
Apply efficiency to motors, generators, solar panels, wind turbines and stations to find output, input or area.
Explain losses and compare system designs using useful energy, wasted transfers and realistic efficiency limits.

[Maximum number: 3]

This question is in two parts. Part 1 is about renewable energy. Part 2 is about nuclear energy and radioactivity.

A small coastal community decides to use a wind farm consisting of five identical wind turbines to generate part of its energy. At the proposed site, the average wind speed is $8.5 \mathrm{~m} \mathrm{~s}^{-1}$ and the density of air is $1.3 \mathrm{~kg} \mathrm{~m}^{-3}$ . The maximum power required from the wind farm is 0.75 MW . Each turbine has an efficiency of 30 %.

Determine the diameter that will be required for the turbine blades to achieve the maximum power of 0.75 MW .

total wind power required $=\frac{750000}{0.3}$ ;

Marking guidance:

maximum wind power required per turbine, $P=\frac{750000}{5 \times 0.3}(=500 \mathrm{~kW})$ ;
$d=\left(\frac{8 P}{\rho \pi v^{3}}=\right)^{\frac{1}{2}} 40(\mathrm{~m}) ;$
[3]
Award [1 max] for an answer of 48.9(m) as it indicates 5 and 0.3 ignored.
Award [2 max] for 22(m) as it indicates 0.3 ignored.
Award [2 max] for 89(m) as it indicates 5 ignored.

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A.3.13—Efficiency question 1