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Date May 2012 Marks available 5 Reference code 12M.2.SL.TZ1.4
Level Standard level Paper Paper 2 Time zone Time zone 1
Command term Deduce and State Question number 4 Adapted from N/A

Question

This question is in two parts. Part 1 is about wind power. Part 2 is about radioactive decay.

Part 1 Wind power

Outline in terms of energy changes how electrical energy is obtained from the energy of wind.

[2]
a.

Air of density ρ and speed v passes normally through a wind turbine of blade length r as shown below.

(i) Deduce that the kinetic energy per unit time of the air incident on the turbine is

\[\frac{1}{2}\pi \rho {r^2}{v^3}\]

(ii) State two reasons why it is impossible to convert all the available energy of the wind to electrical energy.

[5]
b.

Air is incident normally on a wind turbine and passes through the turbine blades without changing direction. The following data are available.

Density of air entering turbine = 1.1 kg m–3
Density of air leaving turbine = 2.2 kg m–3
Speed of air entering turbine = 9.8 m s–1
Speed of air leaving turbine = 4.6 m s–1
Blade length = 25 m

Determine the power extracted from the air by the turbine.

[3]
c.

A wind turbine has a mechanical input power of 3.0×105W and generates an electrical power output of 1.0×105W. On the grid below, construct and label a Sankey diagram for this wind turbine.

[3]
d.

Outline one advantage and one disadvantage of using wind turbines to generate electrical energy, as compared to using fossil fuels.

 

Advantage:

 

Disadvantage:

[2]
e.

Markscheme

kinetic energy of wind transferred to (rotational) kinetic energy of turbine/blades;
kinetic energy changed to electrical energy in generator/dynamo;
Generator/dynamo must be mentioned.

a.

(i) volume of cylinder of air passing through blades per second =vπr2;
mass of air incident per second=ρvπr2;
kinetic energy per second= \(\frac{1}{2}m{v^2}\);
leading to \(\frac{1}{2}\pi \rho {r^2}{v^3}\)
Award [3] for answers that combine one or more steps.

(ii) the speed of the air/wind cannot drop to zero;
wind turbulence / frictional losses in turbine/any moving part / resistive
heating in wires;

b.

kinetic energy per second of air entering turbine \( = \frac{1}{2}\pi  \times 1.1 \times {25^2} \times {9.8^3} = 1.016 \times {10^6}\);
kinetic energy per second of air leaving turbine \( = \frac{1}{2}\pi  \times 2.2 \times {25^2} \times {4.6^3} = 2.102 \times {10^5}\);
power extracted \( = 1.0 \times {10^6} - 2.1 \times {10^5} = 8.062 \times {10^5} \approx 8.1 \times {10^5}{\rm{W}}\);

c.

correct shape of diagram (allow multiple arrows if power loss split into different components);
relative width of arrows correct;
labels correct;

d.

Advantage:
wind is renewable so no resources used up / wind is free / no chemical pollution / no carbon dioxide emission / does not contribute to greenhouse effect / is “scalable” i.e. many sizes of turbine possible;

Disadvantage:
expensive initial cost / large land area needed / wind not constant / effect on movement of birds / aesthetically unpleasant / noise pollution / high maintenance costs / best locations far from population centres / low energy density;

Accept any other suitable advantage or disadvantage.

e.

Examiners report

[N/A]
a.
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b.
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c.
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d.
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e.

Syllabus sections

Core » Topic 8: Energy production » 8.1 – Energy sources
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