Unit 8 Powerpoint

Agenda:

• _{Energy, Power & Climate Change}

Types of Energy

Heat Chemical

Light Gravitational

Sound Elastic/strain

Kinetic Nuclear

Electric

The Law of Conservation of

Energy

Energy can be changed

(transformed) from one

type to another, but it can

never be made or

This means that

the total amount of energy in the

Energy Flow diagrams

We can write energy flow diagrams to show the energy changes that occur in a given

situation.

For example, when a car brakes, its kinetic energy is transformed into heat energy in the brakes.

Kinetic heat

Other examples

When a rocket launches.

Chemical kinetic gravitational

sound

Energy degradation!

In any process that involves energy transformations, the

energy that is transferred to the surroundings (thermal energy) is no longer available to perform

Energy transfer (change)

A lamp turns

electrical energy into heat and

Sankey Diagram

Sankey Diagram

Sankey Diagram

Notice that the total amount of energy

Efficiency

Efficiency

Efficiency is defined as

Example

Efficiency = 75 = 0.15

Energy efficient light bulb

Efficiency = 75 = 0.75

100 _{That’s much}

Energy Density

• _{The energy that can be obtained from a unit}

mass of the fuel

• _J•kg-1

• _{If the fuel is burnt the energy density is}

Energy density

• _{Coal - 30 MJ.kg}-1

• _{Wood - 16 MJ.kg}-1

• _{Gasoline – 47 MJ.kg}-1

Hydroelectric energy density?

• _{Imagine 1 kg falling 100m.}

• _{Energy loss = mgh = 1x10x100 = 10}3 J

• _{If all of this is turned into electrical energy}

it gives an “energy density” of the “fuel” of

Electromagnetic induction

If a magnet is

moved inside a coil an electric current is induced

Electromagnetic induction

A electric current is induced because the

Generator/dynamo

A generator

works in this way by rotating a coil in a magnetic

Non-renewable

• _{Finite (being depleted – will run out)}

• _{In general from a form of potential energy}

Renewable

• _{Mostly directly or indirectly linked with the}

sun

World energy production

Fuel % total energy

production CO2_g.MJ emission -1

Oil 40 70

Natural gas 23 50

Coal 23 90

Nuclear 7

-Hydroelectric 7

-Electricity production

Fossil fuels

In electricity production they are burned, the heat is used to heat water to make

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 (finite)}

• _{Burning coal can cause acid rain} • _{Oil spillages etc.}

• _{Contribute to the greenhouse effect by}

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

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

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

Uranium

Uranium 235 has a large unstable nucleus.

Capture

Capture

Fission

The Uranium 236 is very unstable and splits

Free neutrons

As well as the two smaller nuclei (called

Fission

Chain Reaction

If there is enough uranium (critical mass) a

chain reaction occurs. Huge amounts of

energy are released very quickly.

Bang!

Controlled fission

The chain reaction can be controlled

using control rods

and a moderator.

Fuel rods

• _{In a Uranium reactor these contain Enriched}

Uranium (the percentage of U-235 has been

Moderator

This slows the free neutrons down, making them easier to absorb by the uranium 235 nuclei. Graphite or water is normally used.

Control rods

Heat

Heat

This heat is used to heat water (via a heat

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)

Nuclear power - Advantages

• _{High power output}

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}

The solar constant

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

The solar constant

For the earth this is 1400 W•m-2 and is called the solar constant

The solar constant

The solar constant

This 1400 W•m-2 can only shine on the cross sectional area of the earth as seen from the sun.

Area = πr

However, as the earth turns this is spread over the TOTAL surface area

The solar constant

Therefore the average intensity of the sun falling on the earth = (πr_e2/4πr

e2) 1400 W•m-2

Solar power - advantages

• _{“Free” once built} • _Renewable

Solar power - disadvantages

• _{Only works during the day} • _{Affected by cloudy weather} • _{Low power output}

Water storage in lakes

Pumped storage

• _{Excess electricity can be used to pump}

Tidal water storage

• _{Tide trapped behind a tidal barrage. Water}

Hydroelectric - Advantages

• _{“Free” once built} • _Renewable

Hydroelectric - disadvantages

• _{Very dependent on location}

Wind power

Wind moving at speed

v, cross

sectional area of turbines =

A

V

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

A

Mass of air per second = ρAv

If all kinetic energy of air is transformed by the turbine, the amount of energy produced per second = ½mv2 _{= ½ρAv}3

Wind power - advantages

• _{“Free” once built} • _Renewable

• _Clean

Wind power - disadvantages

• _{Works only if there is wind!} • _{Low power output}

• _{Unsightly (?) and noisy}

OWC

Modeling waves

• _{We can simplfy the mathematics by}

modeling square waves.

λ L

Modeling waves

• _{If the shaded part is moved down, the sea}

becomes flat.

λ L

Modeling waves

• _{The mass of water in the shaded part =}

Volume x density = Ax(λ/2)xLxρ = AλLρ/2

λ L

Modeling waves

• Loss of E_p of this water = mgh = = (AλLρ)/

2 x g x A = A2gLρ(λ/2)

λ L

Modeling waves

• Loss of E_p of this water = mgh= A2gLρ(λ/2)

• _{# of waves passing per unit time = f = v/λ}

λ L

Modeling waves

• Loss of E_p per unit time = A2gLρ(λ/2) x v/λ

• _{= (1/2)A}2Lρgv

λ L

Modeling waves

• _{The maximum power then available per}

unit length is then equal to = (1/2)A2ρgv

λ L

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

Wave power - Advantages

• _{“Free” once built}

• _{Reasonable energy density} • _Renewable

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}

Radiation

from the

Sun

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}

Black-body radiation

• _{http://phet.colorado.edu/sims/blackbody-sp}

Wien’s law

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

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

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}

The Sun

The sun emits electromagnetic waves

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.

Albedo

• _{The Albedo of a body is defined as the ratio}

of the power of radiation reflected or

Albedo

Absorbed by the earth

Around 70% reaches the ground and is absorbed by the earth’s surface.

Absorbed by the earth

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

Temperature of the earth with no

atmosphere?

• _{Power incident on earth = 1.75 x 10}17 W

• _{Since the albedo is 30%, 70% of the}

incident power will be absorbed by the Earth

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;

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

Temperature of the earth with no

atmosphere?

T = 255 K (-18°C)

Absorbed by the earth

Infrared

Absorbed

• _{Various gases in the atmosphere can absorb}

radiation at this longer wavelength (resonance)

Greenhouse gases

• _{These gases are known as “Greenhouse”}

gases. They include carbon dioxide, methane, water and N₂O.

Re-radiated

• _{These gases in the atmosphere absorb the}

Balance

There exists a balance between the energy absorbed by the earth (and its atmosphere) and the energy emitted.

Balance

This means that normally the earth has a fairly constant average temperature

(although there have been big changes over

thousands of years)

Balance

Without this normal “greenhouse effect” the earth would be too cold to live on.

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

What might happen?

What might happen?

• _{Higher sea levels and flooding of low lying}

Coefficient of volume expansion

• _{Coefficient of volume expansion is defined}

Coefficient of volume expansion

Definition

Coefficient of volume expansion is the

fractional change in volume per unit temperature change.

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

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 10}18 _m3

ΔV = γV₀Δθ

ΔV = 2 x 10-4 _{x 1.33 x 10}18 _{x 2 = 5.3 x 10}14 _m3

Δh = ΔV/A = 5.3 x 1014_{/3.6 x 10}14 _{= 1.5 m}

What else might happen?

• _{More extreme weather (heatwaves,}

What might happen?

What might happen?

Evidence?

• _{Ice core research} • _{Weather records}

Other possible causes of global

warming?

• _{Increase in solar activity}

• _{Volcanic activity increasing CO2}

concentrations

Surface heat capacitance C

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.

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 1m}2 of lake receives 340 J.s-1

• Energy needed to raise 1m2 by 2 K = Q =

AC_sΔT = 1 x 4.2 x 108 x 2 = 8.4 x 108 J

• _{Time = Energy/power = 8.4 x 10}8/340 =

2500000 seconds = 29 days

• _{Sun only shines approx 12 hours a day so}