Electricity production

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 MWIn one second, Q = mcΔT

740 x 106 = m x 4200 x 5m = 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.

FissionThe Uranium 236 is very unstable and splits into two smaller nuclei (this is called nuclear fission)

FissionThe 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.

HeatThis 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

AVolume of air going through per second = Av

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

AMass of air per second = ρAv

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.

λ

L

2A

Modeling waves

• If the shaded part is moved down, the sea becomes flat.

λ

L

2A

Modeling waves

• The mass of water in the shaded part = Volume x density = Ax(λ/2)xLxρ = AλLρ/2

λ

L

2A

Modeling waves

• Loss of Ep of this water = mgh = = (AλLρ)/2 x g x A = A2gLρ(λ/2)

λ

L

2A

Modeling waves

• Loss of Ep of this water = mgh= A2gLρ(λ/2)• # of waves passing per unit time = f = v/λ

λ

L

2A

Modeling waves

• Loss of Ep per unit time = A2gLρ(λ/2) x v/λ• = (1/2)A2Lρgv

λ

L

2A

Modeling waves

• The maximum power then available per unit length is then equal to = (1/2)A2ρgv

λ

L

2A

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

• http://phet.colorado.edu/sims/blackbody-spectrum/blackbody-spectrum_en.html

Need to “learn” this!

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 law5.0 x 10-7 x T = 2.9 x 10-3

T = 5800 K

Spectral Class Colour Temperature/KO 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

Infrared

This absorbed solar energy is re-radiated at longer wavelengths (in the infrared region of the spectrum)

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 WAt 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

Infrared

This absorbed solar energy is re-radiated at longer wavelengths (in the infrared region of the spectrum) http://phet.colorado.edu/en/simulation/greenhouse

Absorbed

• Various gases in the atmosphere can absorb radiation at this longer wavelength (resonance)

C

O

O

C

H

HH

HThey vibrate more (become hotter)

HHO

Greenhouse gases

• These gases are known as “Greenhouse” gases. They include carbon dioxide, methane, water and N2O.

C

O

O

C

H

HH

HHH

O

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.

ExampleThe 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 mEvaporation? 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 cl

imate 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.