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Electricity production
Generally (except for solar cells) a turbine
is turned, which turns a generator, which
makes electricity.
Fossil fuels
Fossil fuels
In electricity production they are burned,
the heat is used to heat water to make
steam, the moving steam turns a turbine etc.
Fossil fuels - Advantages
• Relatively cheap
• High energy density
• Variety of engines and devices use them
directly and easily
• Extensive distribution network in place
Fossil fuels - Disadvantages
• Will run out
• Pollute the environment (during mining
sulphur and heavy metal content can be
washed by rain into the environment)
• Oil spillages etc.
• Contribute to the greenhouse effect by
releasing greenhouse gases
Example question
• A coal powered power plant has a power
output of 400 MW and operates with an
overall efficiency of 35%
A coal powered power plant has a power output of 400
MW and operates with an overall efficiency of 35%
• Calculate the rate at which thermal energy
is provided by the coal
A coal powered power plant has a power output of 400
MW and operates with an overall efficiency of 35%
• Calculate the rate at which thermal energy
is provided by the coal
Efficiency = useful power output/power input
Power input = output/efficiency
Power input = 400/0.35 = 1.1 x 103 MW
A coal powered power plant has a power output of 400
MW and operates with an overall efficiency of 35%
• Calculate the rate at which coal is burned
(Coal energy density = 30 MJ.kg-1)
A coal powered power plant has a power output of 400
MW and operates with an overall efficiency of 35%
• Calculate the rate at which coal is burned (Coal
energy density = 30 MJ.kg-1)
1 kg of coal burned per second would produce 30
MJ. The power station needs 1.1 x 103 MJ per
second. So
Mass burned per second = 1.1 x 103/30 = 37 kg.s-1
Mass per year = 37x60x60x24x365 = 1.2 x 109 kg.yr-1
A coal powered power plant has a power output of 400
MW and operates with an overall efficiency of 35%
• The thermal energy produced by the power plant is
removed by water. The temperature of the water must
not increase by more than 5 °C. Calculate the rate of
flow of water.
A coal powered power plant has a power output of 400
MW and operates with an overall efficiency of 35%
• The thermal energy produced by the power plant is
removed by water. The temperature of the water must
not increase by moe than 5 °C. Calculate the rate of
flow of water.
Rate of heat loss = 1.1 x 103 – 0.400 x 103 = 740 MW
In one second, Q = mcΔT
740 x 106 = m x 4200 x 5
m = 35 x 103 kg
So flow needs to be 35 x 103 kg.s-1
Nuclear Fission
Uranium
Uranium 235 has a large unstable nucleus.
Capture
A lone neutron hitting the nucleus can be
captured by the nucleus, forming Uranium
236.
Capture
A lone neutron hitting the nucleus can be
captured by the nucleus, forming Uranium
236.
Fission
The Uranium 236 is very unstable and splits
into two smaller nuclei (this is called
nuclear fission)
Fission
The Uranium 236 is very unstable and splits
into two smaller nuclei (this is called
nuclear fission)
Free neutrons
As well as the two smaller nuclei (called
daughter nuclei), three neutrons are released
(with lots of kinetic energy)
Fission
These free neutrons can strike
more uranium nuclei, causing
them to split.
Chain Reaction
If there is enough uranium (critical mass) a
chain reaction occurs. Huge amounts of
energy are released very quickly.
Bang!
This can result in a nuclear explosion!YouTube nuclear bomb 4
Controlled fission
The chain reaction
can be controlled
using control rods
and a moderator.
The energy can then
be used (normally to
generate electricity).
Fuel rods
• In a Uranium reactor these contain Enriched
Uranium (the percentage of U-235 has been
increased – usually by centrifuging)
Moderator
This slows the free neutrons down, making
them easier to absorb by the uranium 235
nuclei. Graphite or water is normally used.
1 eV neutrons
are ideal)
Control rods
These absorb excess neutrons,making sure
that the reaction does not get out of control.
Boron is normally used.
Heat
The moderator gets hot from the energy it
absorbs from the neutrons.
Heat
This heat is used to heat water (via a heat
exchanger), to make steam, which turns a turbine,
which turns a generator, which makes electricity.
Useful by-products
Uranium 238 in the fuel rods can also
absorb neutrons to produce plutonium 239
which is itself is highly useful as a nuclear
fuel (hence breeder reactors)
It makes more
fuel!!!
Nuclear Power
That’s how a nuclear power station works!
Nuclear power - Advantages
• High power output
• Large reserves of nuclear fuels
• No greenhouse gases
Nuclear power - disadvantages
• Waste products dangerous and difficult to
dispose of
• Major health hazard if there is an accident
• Problems associated with uranium mining
• Nuclear weapons
Solar power
The solar constant
The solar constant
The sun’s total power output is 3.9 x 1026 W!
The solar constant
The sun’s total power output is 3.9 x 1026 W!
Only a fraction of this power actually reaches
the earth, given by the formula
I (Power per unit area) = P/4πr2
For the earth this is 1400 W.m-2 and is called
the solar constant
The solar constant
For the earth this is 1400 W.m-2 and is called
the solar constant
This varies according to the power output of
the sun (± 1.5%), distance from sun (± 4%),
and angle of earth’s surface (tilt)
Solar power - advantages
• “Free”
• Renewable
• Clean
Solar power - disadvantages
•
•
•
•
•
Only works during the day
Affected by cloudy weather
Low power output
Requires large areas
Initial costs are high
Hydroelectric power
Water storage in lakes
“High” water has GPE. AS it falls this urns
to KE, turns a turbine etc.
Pumped storage
• Excess electricity can be used to pump
water up into a reservoir. It acts like a giant
battery.
Tidal water storage
• Tide trapped behind a tidal barrage. Water
turns turbine etc.
• YouTube - TheUniversityofMaine's
Channel
Hydroelectric - Advantages
• “Free”
• Renewable
• Clean
Hydroelectric - disadvantages
• Very dependent on location
• Drastic changes to environment (flooding)
• Initial costs very high
Wind power
Wind power
Calculating power
Wind moving at speed v, cross
sectional area of turbines = A
V
A
Wind moving at speed v, cross
sectional area of turbines = A
V
Volume of air going through per second = Av
A Mass of air per second = Density x volume
Mass of air per second = ρAv
Wind moving at speed v, cross
sectional area of turbines = A
V
Mass of air per second = ρAv
A If all kinetic energy of air is transformed by the
turbine, the amount of energy produced per
second = ½mv2 = ½ρAv3
Wind power - advantages
•
•
•
•
“Free”
Renewable
Clean
Ideal for remote locations
Wind power - disadvantages
•
•
•
•
•
Works only if there is wind!
Low power output
Unsightly (?) and noisy
Best located far from cities
High maintainance costs
Wave power
OWC
Oscillating
water column
Modeling waves
• We can simplfy the mathematics by
modeling square waves.
L
2A
λ
Modeling waves
• If the shaded part is moved down, the sea
becomes flat.
L
2A
λ
Modeling waves
• The mass of water in the shaded part =
Volume x density = Ax(λ/2)xLxρ = AλLρ/2
L
2A
λ
Modeling waves
• Loss of Ep of this water = mgh = =
(AλLρ)/2 x g x A = A2gLρ(λ/2)
L
2A
λ
Modeling waves
• Loss of Ep of this water = mgh= A2gLρ(λ/2)
• # of waves passing per unit time = f = v/λ
L
2A
λ
Modeling waves
• Loss of Ep per unit time = A2gLρ(λ/2) x v/λ
• = (1/2)A2Lρgv
L
2A
λ
Modeling waves
• The maximum power then available per unit
length is then equal to = (1/2)A2ρgv
L
2A
λ
Power per unit length
A water wave of amplitude A carries an
amount of power per unit length of its
wavefront equal to
P/L = (ρgA2v)/2
where ρ is the density of water and v stands
for the speed of energy transfer of the wave
Wave power - Advantages
•
•
•
•
“Free”
Reasonable energy density
Renewable
Clean
Wave power - disadvantages
• Only in areas with large waves
• Waves are irregular
• Low frequency waves with high frequency
turbine motion
• Maintainance and installation costs high
• Transporting power
• Must withstand storms/hurricanes
Radiation
from the
Sun
http://www.youtube.com/watch?NR=1&v=1pfqIcSydgE
Black-body radiation
• Black Body - any object that is a perfect
emitter and a perfect absorber of radiation
• object does not have to appear "black"
• sun and earth's surface behave
approximately as black bodies
Black-body radiation
Need to “learn” this!
• http://phet.colorado.edu/sims/blackbodyspectrum/blackbody-spectrum_en.html
Wien’s law
• λmaxT = constant (2.9 x 10-3 mK)
Example
• The sun has an approximate black-body
spectrum and most of its energy is radiated
at a wavelength of 5.0 x 10-7 m. Find the
surface temperature of the sun.
• From Wien’s law
5.0 x 10-7 x T = 2.9 x 10-3
T = 5800 K
Spectral Class
Colour
Temperature/K
O
Blue
25 000 – 50 000
B
Blue - white
12 000 – 25 000
A
White
7 500 – 12 000
F
Yellow - white
6 000 – 7 500
G
Yellow
4 500 – 6 000
K
Yellow - red
3 000 – 4 500
M
Red
2 000 – 3 000
In the astrophysics option you need to remember the
classes and their order. How will you do this?
Spectral classes
Oh be a fine girl….kiss me!
Stefan-Boltzmann law
The amount of energy per second (power)
radiated from a body depends on its surface
area and absolute temperature according to
P = eσAT4
where σ is the Stefan-Boltzmann constant
(5.67 x 10-8 W.m-2.K-4) and e is the
emissivity of the surface ( e = 1 for a black
object)
Example
• By what factor does the power emitted by a
body increase when its temperature is
increased from 100ºC to 200ºC?
Example
• By what factor does the power emitted by a
body increase when its temperature is
increased from 100ºC to 200ºC?
• Emitted power is proportional to the fourth
power of the Kelvin temperature, so will
increase by a factor of 4734/3734 = 2.59
Graph sketching
Global Warming
The Sun
The sun emits electromagnetic waves
(gamma X-rays, ultra-violet, visible light,
infra-red, microwaves and radio waves) in
all directions.
The earth
Some of these waves will reach the earth
Reflected
Around 30% will be reflected by the earth and the
atmosphere. This is called the earth’s albedo
(0.30). (The moon’s albedo is 0.12) Albedo is the
ratio of reflected light to incident light.
30%
Albedo
• The Albedo of a body is defined as the ratio
of the power of radiation reflected or
scattered from the body to the total power
incident on the body.
Albedo
The albedo depends on the ground covering
(ice = high, ocean = low), cloud cover etc.
Absorbed by the earth
Around 70% reaches the ground and is
absorbed by the earth’s surface.
70%
Absorbed by the earth
This absorbed solar energy is re-radiated at
longer wavelengths (in the infrared region
of the spectrum)
Infrared
Temperature of the earth with no
atmosphere?
• Remember the solar constant is around
1360 W.m-2. This can only shine on one
side of the Earth at a time, and since the
silhouette of the earth is a circle, the power
incident = 1360 x πr2
= 1360 x π x (6.4 x 106)2 = 1.75 x 1017 W
Temperature of the earth with no
atmosphere?
• Power incident on earth = 1.75 x 1017 W
• Since the albedo is 30%, 70% of the
incident power will be absorbed by the
Earth
• 70% of 1.75 x 1017 W = 1.23 x 1017 W
Temperature of the earth with no
atmosphere?
Power absorbed by Earth = 1.23 x 1017 W
At equilibrium,
the Power absorbed = Power emitted
Using the Stefan Boltzmann law;
1.23 x 1017 = eσAT4
Temperature of the earth with no
atmosphere?
Using the Stefan Boltzmann law;
1.23 x 1017 = eσAT4
1.23 x 1017 = 1 x 5.67 x 10-8 x 4πr2 x T4
This gives T = 255 K (-18°C)
Temperature of the earth with no
atmosphere?
T = 255 K (-18°C)
This is obviously much colder than the
earth actual temperature. WHY?
Absorbed by the earth
This absorbed solar energy is re-radiated at
longer wavelengths (in the infrared region of
the spectrum)
http://phet.colorado.edu/en/simulation/green
Infrared
house
Absorbed
• Various gases in the atmosphere can absorb
radiation at this longer wavelength
(resonance)
H
O
C
O
O
H
H
H
C
H
H
They
vibrate
more
(become
hotter)
Greenhouse gases
• These gases are known as “Greenhouse”
gases. They include carbon dioxide,
methane, water and N2O.
O
C
O
O
H
H
H
H
C
H
H
Transmittance curves
Re-radiated
• These gases in the atmosphere absorb the
infra-red radiation and re-emit it, half goes
into space but half returns to the earth.
It’s complex!!!
Balance
There exists a balance between the energy
absorbed by the earth (and its atmosphere)
and the energy emitted.
Energy in
Energy out
Balance
This means that normally the earth has a
fairly constant average temperature
(although there have been big changes over
thousands of years)
Energy in
Energy out
Balance
Without this normal “greenhouse effect” the
earth would be too cold to live on.
Energy in
Energy out
Greenhouse gases
• Most scientists believe that we are
producing more of the gases that absorb the
infra-red radiation, thus upsetting the
balance and producing a higher equilibrium
earth temperature. This is called the
enhanced greenhouse effect.
What might happen?
What might happen?
• Polar ice caps melt
What might happen?
• Higher sea levels and flooding of low lying
areas as a result of non-sea ice melting and
expansion of water
Coefficient of volume expansion
• Coefficient of volume expansion is defined
as the fractional change in volume per unit
temperature change
Coefficient of volume expansion
Given a volume V0 at temperature θ0, the
volume after temperature increase of Δθ
will increase by ΔV given by
ΔV = γV0Δθ
Definition
Coefficient of volume expansion is the
fractional change in volume per unit
temperature change.
ΔV = γV0Δθ
Example
The area of the earth’s oceans is about 3.6 x
108 km2 and the average depth is 3.7 km.
Using γ = 2 x 10-4 K-1, estimate the rise in
sea level for a temperature increase of 2K.
Comment on your answer.
Example
The area of the earth’s oceans is about 3.6 x 108 km2 and the average
depth is 3.7 km. Using γ = 2 x 10-4 K-1, estimate the rise in sea level for
a temperature increase of 2K. Comment on your answer.
Volume of water = approx depth x area
= 3.6 x 108 x 3.7
= 1.33 x 109 km3 = 1.33 x 1018 m3
ΔV = γV0Δθ
ΔV = 2 x 10-4 x 1.33 x 1018 x 2 = 5.3 x 1014 m3
Δh = ΔV/A = 5.3 x 1014/3.6 x 1014 = 1.5 m
Evaporation? Greater area cos of flooding? Uniform expansion?
What else might happen?
• More extreme weather (heatwaves,
droughts, hurricanes, torrential rain)
What might happen?
• Long term climate change
What might happen?
• Associated social problems (??)
Evidence?
Evidence?
•
•
•
•
•
Ice core research
Weather records
Remote sensing by satellites
Measurement!
How do ice cores allow researchers to see
climate change? | GrrlScientist | Science |
guardian.co.uk
Surface heat capacitance Cs
Surface heat capacitance is defined as the
energy required to increase the temperature
of 1 m2 of a surface by 1 K. Cs is measured
in J.m-2.K-1.
Q = ACsΔT
Example
• Radiation of intensity 340 W.m-2 is incident
on the surace of a lake of surface heat
capacitance Cs = 4.2 x 108 J.m-2.K-1.
Calculate the time to increase the
temperature by 2 K. Comment on your
answer.
Example
• Radiation of intensity 340 W.m-2 is incident on the surface of a lake of
surface heat capacitance Cs = 4.2 x 108 J.m-2.K-1. Calculate the time to
increase the temperature by 2 K. Comment on your answer.
• Each 1m2 of lake receives 340 J.s-1
• Energy needed to raise 1m2 by 2 K = Q =
ACsΔT = 1 x 4.2 x 108 x 2 = 8.4 x 108 J
• Time = Energy/power = 8.4 x 108/340 =
2500000 seconds = 29 days
• Sun only shines approx 12 hours a day so
would take at least twice as long
Let’s read!
Pages 198 to 211 of SL Physics by Hamper
and Ord.
Pages 434 to 450 of Physics for the IB
Diploma by Tsokos
Homework
• Page 450 Qs 1, 2a, 5, 7, 9, 20,
30.