IB Physics SL A 3 14 Fuel Energy Density Questions

Practise converting fuel energy density, mass, volume, efficiency and power in realistic energy calculations and exam questions.

Exam points

Define and apply fuel energy density as energy available per unit mass or volume with correct units.
Use energy density with mass, volume, efficiency or power to calculate available energy, consumption or operating time from complete evidence.

[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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IB Physics SL A 3 14 Fuel Energy Density Questions question 1