TOPIC 8 SOLUTIONS
Example 1
A power plant produces 500 MW f power.
a) How much energy is produced in one second? Express your answer in (i) j
(ii) kWh
b) How much energy in joules is produced in one year?
a) 5 x 108 J , 140 kWh
b) 1.6 x 1016 J
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Define :
a) Sankey diagram – diagram that represents energy flows
b) Energy degradation – excess energy lost and is “ less useful” and can not
be used to perform mechanical work
c) Non- renewable energy source ( give 2 examples)– finite sources that will
run out e.g : fossil fuels, nuclear
d) Renewable energy source ( give 3 examples ) - energy that can renew
itself eg. : solar, wind, wave - tidal, geothermal, hydroelectricity
e) Energy density ( state unit) – energy that can be obtained from one unit
mass. Jkg-1 . High energy density = high power output
f) Specific Energy – energy , in joules (J), that can be obtained from one Kg
: Jkg-1 .
Example 4:
Explain fig. 1.1 below and why you only get 25% efficiency rating using the
formula for efficiency . Also, explain how much is considered degraded energy:
Sankey diagram representing energy flows. 800 input, 600 degraded, output
useful energy 200.
Efficiency = output energy = 200 = 25 %
Input energy
800
Degraded = 600 can not be used for useful work.
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Example 5:
a) A power station has an output power of 500 MW and overall efficiency of 27%
. It uses natural gas as a fuel. How much input energy is being consumed by the
natural gas?
b) Natural gas has an energy density of 56 MJ kg-1. 1 MW = 1 MJs-1 . Calculate
the rate of consumption of natural gas in the power station in kgs-1 by using the
energy density and the input energy ( in MW) calculated in part a above.
Rate = input energy
specific Energy
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Example 6:
A power plant produces electricity by burning coal, using the thermal energy
produced as input to a steam engine, which makes a turbine turn, producing
electricity. The plant has a power output of 400 MW and operates at an
overall efficiency of 35%.
a) Calculate the rate at which thermal energy is provided by the burning coal.
i.e calculate the energy input that the burning coal provides for the power
plant.
b) Calculate rate at which coal is being burned. Specific Energy of coal is
30MJkg-1.
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a)
Efficiency = output energy
Input energy
Input = 400 = 1143 MW
.35
b) Rate = input energy
specific energy
=
1143 =
30
38.1 kgs-1
Example 7:
A coal burning power plant produces 1.0 GW of electricity. The overall efficiency
of the power plant is 40%. Taking the specific energy of coal to be 30 MJkg-1 ,
calculate the amount of coal that must be burned in one day.
Ans. : 7.2 x 106 kg day-1
note : energy density = specific energy
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Example 8:
This question is about power generation.
(a)
Describe the origin of fossil fuels.
(b)
An electrical power generating station using fossil fuels as its source of
energy has an output of 2 GW. It has been suggested that this station
should be replaced by wind turbines, each providing 0.8 MW of
electrical power.
(i)
State two advantages of the use of wind power.
(ii)
State and explain two disadvantages of using wind turbines to
replace the fossil-fuel generating station.
(c ) List 4 advantages of fossil fuels
(d) List 3 disadvantages of fossil fuels
a)
organic / living matter;
(partial) decomposition;
under conditions of “high”(temperature) and pressure;
(b)
(i)
eg renewable energy source;
no CO2 emissions;
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2
Do not allow “pollution free” / cost.
Award [1] each for any two sensible suggestions.
(ii)
eg large number of turbines required;
covering large area of land;
eg output dependent on wind speed;
so unreliable;
eg change in local climate;
as a result of turbulence;
Award [1] each for any two sensible suggestions and [1] for
each explanation.
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[9]
(c ) cheap , high power output = high specific energy, multi use by variety of
engines, devices, plants, extensive distribution network is in place.
(d) non renewable ( will run out), pollute, contribute to the green house effect
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2. Nuclear Power pp. 420 – 423
Explain basics : Fuel is typically U – 235
Rxn :
n1 + 235 U  236 U  140 Xe + 94 Sr + 2 1 n
0
92
92
54
38
0
Neutron must bombard U 235 to initiate rxn. The rxn is self sustaining and is called a
chain rxn. For rxn to keep going a certain minimum number of U 235 must be
present otherwise the neutrons escape without causing further rxns. – this is called
critical mass. U 235 will only catch the neutrons if they are not moving too fast. The
neutrons that are produced during the rxn aret to fast so they have to be slowed down.
Slowing down the neutrons is achieved by collisions of neutrons with a moderator which
is a material surrounding the fuel rods. The moderator is usually water or graphite.
The fuel rods are the tubes that contain 235. NOTE: if water is the moderator, do
not confuse with the other water that is used as a coolant.
If the rxn gets out of hand, i.e too many neutrons flying around, control rods are used.
These absorb excess neutrons when the rxn begins to get out of hand and are
introduced by the engineer- tech. when needed. An atomic bomb has no control rods.
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Example 9 :
This question is about nuclear power.
(a)
A fuel often used in nuclear reactors is uranium. Explain why uranium is a
non-renewable energy source.
(b)
One nuclear reaction that takes place in a reactor is
1
235
235
140
94
0 n  92 U 92 U 54 Xe  38 Sr
 x10 n .
(i)
State the number x of neutrons produced in this reaction.
(ii)
Using the equation explain what is meant by a chain reaction.
(iii)
Explain how, in a reactor, the production of energy in a chain reaction is
controlled.
(c)
Outline how the energy produced in fission reactions is transferred to thermal
energy.
(d)
State one advantage of nuclear power production compared to fossil fuel
power production.
(e)
When a uranium nucleus fissions, approximately 180 MeV of energy is
released. The overall efficiency of a nuclear reactor is 23 and its output
power is 450 MW.
Calculate the number of fissions required per second
(a)
non renewable since the stocks of uranium cannot be replenished/will run out;
1
(b)
1
(i)
x = 2;
(ii)
each neutron can fission another uranium nucleus;
The neutrons produced in this fission can produce further fissions
and so on;
Accept the use of an appropriate diagram.
(iii) use of control rods to absorb excess neutrons;
some further detail eg lowering or raising control rods to
control rate of absorption;
2
2
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(c)
(d)
K.E. of fission fragments and neutrons;
transferred to thermal energy in core and moderator;
thermal energy carried away by coolant / reference to heat
exchange in reactor;
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no greenhouse gases are emitted / fuel source will last longer / no
need for tall chimneys / any other suitable point;
1
(e) 180 MeV converted to J : 180  106  1.6  1019J = (2.9  1011J);
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Example 10
Example 11: A
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Example 12:
Critical mass refers to the amount of fissile material that A
A. will allow fission to be sustained.
B. is equivalent to 235 g of uranium.
C. will produce a growing chain reaction.
D. is the minimum mass necessary for fission to take place
Example 13:
The commercial production of energy by nuclear fusion is not yet possible mainly due to
difficulties with C
A.
obtaining plentiful supplies of a suitable fuel.
B.
reaching the high temperatures required.
C.
confining the hot plasma.
D.
disposing of the radioactive waste products.
Example 14 :
List 3 advantages and 4 disadvantages of nuclear energy :
3 adv. : high power output; large reserves of nuclear fuels; do not produce
greenhouse gases
4 disadv. : non-renewable, radioactive waste difficult to dispose; major public
health hazard should something go wrong – Japaj, Russia; problems associated
with uranium mining; used for nuclear weapons
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Example 15
This question is about solar power. NOTES
(a)
Describe, in terms of energy transformations, the difference between a
photovoltaic cell and an active solar heater.
(b)
A photovoltaic cell of area 6.5  10–4 m2 is situated on the roof of a house.
The cell has an efficiency of 8%. At a time when the power of the solar
radiation incident on the photovoltaic cell is a maximum, the cell delivers a
power of 47 W to the external circuit.
(i)
Calculate the amount of power per square meter of 1 photovoltaic cell
delivered after loss due to the efficiency rating.
Answer:
(a)
photovoltaic cell: light energy / energy from the Sun is converted into
electrical energy;
active solar heater: light energy / energy from the Sun is converted into
thermal energy / heat;
(b)
47 W x 8 % = 3.76 W
Wm-2 = 3.76 W
6.5  10–4 m2
(c)
2
= 5785 Wm-2 = amount of watts delivered by
1 m2
(ii)
the amount of sunlight varies with season / time of day /
(i)
If 1 cell delivers 5785 W then number of cells needed for 3 kW =
30000W x 1 cell
= 7979 cells
3.76 W
(ii) active solar heater;
requires less area / any other relevant reason eg cost / storage problems;
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Example 16:
Find the power developed when water in a stream with flow rate 50Ls-1 falls from a
height of 15m.
Ans. 7.4 x 106 W = 7.4 MW
NOTE : MW correct
NOT KW
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Example 17 : A
Slope = H0 / T = distance / time = velocity. Power prop to v: P = Fv
Example 18 :
List 3advantages and 3 disadvantages of hydroelectricity.
Adv.: “free” , renewable - inexhaustible, clean
Disadv. : dependent on location, requires drastic changes in the environment, initial
costs high.
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Example 19
This question is about wind power.
The maximum theoretical wind power P for air of speed v moving normally
through area A where  is the density of air is given by
P
(a)
(i)
ρ Av 3
.
2
Air of density 1.3 kg m–3 and speed of 9.0 m s–1 is incident on a
wind turbine having blades of diameter 15 m. Calculate the
maximum wind power incident on the turbine.
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(ii)
State why it is impossible in practice to extract all of the power P
in (i) from the air.
(iii) State two reasons why wind turbines are not placed close to one
another.
(ii)
the speed of air (mass) cannot drop to zero / OWTTE;
(iii) 1.
2.
1
idea of less KE available for the next turbine;
idea of turbulence;
Adv. and disadv. Of wind power ;
Adv.: wind is a renewable source of energy / clean source of energy;
disadvantage: number of turbines required is very large (about 270) /
noise / ugly site / ecological impact;
Wave p. 428
P = pg A2 v
L
2
Power/ length of wave front = density x gravity x Amplitude2 x speed
2
List 3 advantages and 6 disadvantages of wave power.
Adv. : “ free” , reasonable specific energy , renewable - “inexhaustible”, clean
Disadv. : location, irregular wave patterns, matching f of waves and turbine,
maintenance, transporting power, hurricanes
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Example 20 :
By what factor does the power emitted by a body increase when the
temperature is increased from 1000 C to 2000 C ?
Be careful. Even though it doubles in C doesn’t mean it doubles in K
Convert to K  K = C + 273
So temp. increases from 373 to 473 of by a factor of 473 = 1.26
373
P = e σ AT4
P = (T)4
P = ( 1.26) 4 = P increases by a factor of 2.59
Example 21 :
By what factor does the rate of radiation from a body increase when the
temperature is increased from 50 C to 100 C
50C = 323K
100 C = 373 K
T increases by 373 = 1.155
323
P = T4 = ( 1.155)4 = 1.8
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Example 22
Two black bodies X and Y are at different temperatures. The temperature of body Y is
higher than that of body X. Which of the following shows the black body spectra for
the two bodies?
Answer A
CURVE.
: Y has to have a shorter wavelength AT EVERY POINT ON THE
Example 23 :
Calculate the average albedo of earth if the average incident solar
radiation is 350 Wm-2 and the average absorbed radiation is 250 Wm -2.
α = total scattered OR reflected power
total incident power
Reflected radiation = total incident – absorbed = 100
So
α = 100 = 0.29
350
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Example 24 :
The diagram below shows a simplified model of the energy balance for Earth.
The albedo of the Earth according to this model is equal to
A.
2
.
340
B.
100
.
340
C.
238
.
340
D.
240
.
340
α = total scattered OR reflected power
total incident power
Answer : B
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Example 25 :
It is hypothesized that global warming may lead to significant changes in the average sealevel. This hypothesis assumes that
A.
average rainfall will increase.
B.
icebergs will melt.
C.
glaciers will melt.
D.
the rate of evaporation of seawater will increase.
Answer : B
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