IB Physics SL A.3.14 Fuel energy density

Practise relating fuel energy density to power, fuel volume and mass so you can move confidently between J, kg and m^3.

Exam points

calculate fuel volume from energy needed and energy density, checking the final unit is m^3 rather than J or kg
combine useful power, efficiency and fuel consumption rate to determine an unknown energy density or usage rate
distinguish energy density from specific energy when comparing fuels given both mass and volume information

[Maximum number: 2]

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 %.

Currently, a nearby coal-fired power station generates energy for the community. Less coal will be burnt at the power station if the wind farm is constructed.

The energy density of coal is $35 \mathrm{MJ} \mathrm{kg}^{-1}$ . Estimate the minimum mass of coal that can be saved every hour when the wind farm is producing its full output.

mass of coal per second $(=0.0214 \mathrm{~kg})$ ;
$77.1(\mathrm{~kg})$ ;
or
energy saved per hour $=0.75 \times 3600\left(=2700 \mathrm{MJ} \mathrm{h}^{-1}\right)$ ;
mass of coal saved $=\left(\frac{2700}{35}=\right) 77.1(\mathrm{~kg})$ ;

Marking guidance:

Award [2] for a bald correct answer.

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A.3.14—Fuel energy density question 1