IB Physics SL A 3 13 Efficiency Questions

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

Exam points

Calculate efficiency as η = Eoutput/Einput or Poutput/Pinput.
Use efficiency with energy or power data and Sankey representations to determine useful output, input or losses from complete evidence.

[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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IB Physics SL A 3 13 Efficiency Questions question 1