IB Physics SL A.3.13 Efficiency

Improve efficiency calculations by connecting useful output to total input and using power or energy data from realistic devices.

Exam points

use efficiency = useful output/input to find a missing power, energy, height, or fuel mass
for panels or turbines, combine efficiency with area, intensity, or speed before comparing output
state wasted energy clearly and keep power or energy units consistent when quoting efficiency

[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