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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

12πρr2v3

(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= 12mv2;
leading to 12πρr2v3
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 =12π×1.1×252×9.83=1.016×106;
kinetic energy per second of air leaving turbine =12π×2.2×252×4.63=2.102×105;
power extracted =1.0×1062.1×105=8.062×1058.1×105W;

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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