Topic 8 Energy Power and Climate Change

IB 12

1

Power Generation in a typical electrical power plant

a) Some fuel is used (coal, natural gas, oil, uranium) to release thermal energy which is used to boil water to make steam.

b) Generator (Dynamo) - Steam turns turbines attached

to coils of wire which turn in a magnetic field inducing an alternating potential difference.

c) Potential difference is stepped up by transformers in

order to reduce I2R loss of power in transmission lines then stepped down for consumer use.

Energy and Power

What are the energy transformations that take place?

Chemical (nuclear) energy in fuel

thermal energy in steam

rotational mechanical energy/kinetic energy in turbine

electrical energy in generator

Thermal energy hot gases go out chimney/stack

Thermal energy radiation and convection from boiler

Thermal energy friction in the generator

Degraded energy: energy transferred to the surroundings that is no longer available to do useful work cant be converted into other forms

IB 12

2

Fuel Typical Efficiency Coal 30-35%

Natural Gas 50%

Oil 30-35%

Second Law of Thermodynamics:

1) The total entropy of the universe is increasing. 2) No cyclical process (engine) is ever 100% efficient. Some energy is transferred

out of the system (lost to the surroundings) as unusable energy (degraded energy).

1. Thermal energy can be completely converted to work in a single process.

Example: isothermal expansion Q = U + W U = 0 so Q = W

2. A continuous conversion of thermal energy into work requires a cyclical process.

Why does the generation of electrical power involve the degradation of energy?

Sankey diagrams (energy flow diagrams): used to keep track of energy transfers and transformations

1) Thickness of arrow is proportional to amount of energy. 2) Degraded energy points away from main flow of energy.

3) Total energy in = total energy out.

Output 30% Electrical energy Input

100% Chemical energy

10% Thermal energy Friction in dynamo

20% Thermal energy boiler

40% Thermal energy exhaust gas out chimney

Fuel boiler dynamo

IB 12

3

NOTE: In most instances, the prime energy source for world energy is . . . the Sun.

This histogram shows the relative proportions of world use of the different types of energy sources, though it will

vary from country to country.

Fossil fuels: coal, oil, natural gas, peat Origins of fossil fuels: organic matter decomposed under conditions of high temperature and pressure over millions of years

Non-renewable fuels: rate of production of fuel is much smaller than rate of usage so fuel will be run out - limited supply

Renewable fuels: resource that cannot be used up or is replaced at same rate as being used

Fuel: source of energy (in a useful form) How does a fuel work? A fuel releases energy by changing its chemical (or nuclear) structure. Chemical (or nuclear) bonds are broken reducing the fuels internal potential energy but increasing the kinetic energy of the substances particles which is seen macroscopically as an increase in the temperature of the substance. It is this thermal energy that is used to heat the water that will change to steam to turn the generators turbines.

Fuels

Type of fuel Renewable? CO2 emissions?

Fossil fuels No Yes

Nuclear No No

Hydroelectric Yes No

Wind Yes No

Solar Yes No

Wave Yes No

Exceptions: nuclear, tidal (Moon)

IB 12

4

Fossil Fuel Power Production

Historical and geographical reasons for the widespread use of fossil fuels:

1. industrialization led to a higher rate of energy usage (Industrial Revolution) 2. industries developed near large deposits of fossil fuels (coal towns)

Transportation and storage considerations:

Use of fossil fuels for generating electricity Advantages: Disadvantages:

1. high energy density 2. relatively easy to transport

3. cheap compared to other sources

4. power stations can be built anywhere

5. can be used in the home

1. combustion produces pollution, especially SO2 (acid rain) 2. combustion produces greenhouse gases (CO2)

3. extraction (mining, drilling) damages environment

4. nonrenewable

5. coal-fired plants need large amounts of fuel

3. Power stations using coal and steel mills are usually located near coal mines.

Advantages: minimizes shipping costs

Disadvantages: environmental impact (strip mining), mine cave-ins

2. Many oil refineries are located near the sea close to large cities. Oil is transported via ships, trucks, and pipelines.

Advantages: workforce and infrastructure in place, easy access to shipping Disadvantages: oil spills and leakage, hurricanes, terrorist activities

1. Natural gas is usually transported and stored in pipelines.

Advantages: cost effective

Disadvantages: unsightly, susceptible to leaks, explosions, terrorist activities, political instability (withholding use of pipelines or terminals for political reasons)

IB 12

5

Energy density of a fuel: the ratio of the energy released from the fuel to the mass of the fuel consumed

Units: J/kg

Use: to compare different types of fuels

How is choice of fuel influenced by energy density? Fuels with higher energy density cost less to transport and store

Fuel Energy Density (MJ/kg)

Fusion fuel 300,000,000 Uranium-235 90,000,000 Natural gas 53.6 Gasoline (Petrol) 46.9 Diesel 45.8 Biodiesel 42.2 Crude oil 41.9 Coal 32.5 Sugar 17.0 Wood 17.0 Cow dung 15.5 Household waste 10

Formula: De = E/m

1. An oil-fired power station produces 1000 MW of power.

b) Estimate how much oil the power station needs each day.

a) How much energy will the power station produce in one day?

6

13

(1000 x 10 )(24 3600)8.6 10

EPt

E PtE W xE x J

=

=

=

=

13

14

useful outtotal in

8.6 10.35

2.46 10

out

in

in

in

EeffE

x JE

E x J

= =

=

=

146

6

2.46 1041.9 10

5.9 10

eEDm

J x Jxkg m

m x kg

=

=

=

IB 12

6

2. A 250 MW coal-fired power plant burns coal with an energy density of 35 MJ/kg. Water enters the cooling tower at a temperature of 350 K and leaves at a temperature of 293 K and the water flows through the cooling tower at a rate of 4200 kg/s.

a) Calculate the thermal energy removed from the water in the cooling towers each second.

b) Assuming the only significant loss of energy is this thermal energy of the water, calculate the energy produced by the combustion of coal each second.

c) Calculate the mass of coal burned each second.

9

9

1.0 101

1.0 10 1000

EPtx JPs

P x W MW

=

=

= =

3

9

(4200 )(4.19 10 )(350 293)

1.0 10

Q mc TJQ kg xkgK

Q x J

=

=

=

1000 MJ + 250 MJE 1250

in out

in

in

E EE

MJ

=

=

=

useful outtotal in

2501250.20

out

in

PeffP

MWeffMW

eff

= =

=

=

66 1250 1035 10

36

eEDmJ x Jxkg m

m kg

=

=

=

IB 12

7

Nuclear Energy

Most common source: fissioning of uranium-235 with conversion of some mass into energy

235 1 141 92 192 0 56 36 03U n Ba Kr n+ + +

Process:

a) unstable uranium nucleus is bombarded with a neutron and splits into two smaller nuclei and some neutrons

Why use neutrons? Neutral, not repelled by nucleus

b) rest mass of products is less than reactants so

some matter is converted into energy

Form of energy: KE of products (thermal energy)

c) released neutrons strike other uranium nuclei

causing further fissions

1) A particular nuclear reactor uses uranium-235 as its fuel source. When a nucleus of uranium-235 absorbs a neutron, the following reaction can take place:

235 1 144 90 192 0 54 38 0U n Xe Sr x n+ + +

a) How many neutrons are produced in the reaction? 2

b) Use the information to show that the energy released in the reaction is approximately 180 MeV.

235 5 292

1 20144 5 254

90 5 238

rest mas of 2.1895 x 10 MeV c

rest mas of 939.56 MeV c



UnXeSr

=

=

=

=

IB 12

8

2. The energy released by one atom of carbon-12 during combustion is approximately 4 eV. The

energy released by one atom of uranium-235 during fission is approximately 180 MeV.

a) Based on this information, determine the ratio of the energy density of uranium-235 to that of carbon-12. (Then, check your answer with the given table of energy densities.)

b) Based on your answer above, suggest one advantage of uranium-235 compared with fossil fuels.

Higher energy density implies that uranium will produce more energy per kilogram less fuel needed to produce the same amount of energy

76 U-235 7.38 10 2.3 10

C-12 32.2e

e

D x xD

= =

23

25

= x molar mass

1mass = x .235 kg6.02 10

mass=3.90x10

A

NmassN

xkg

23

26

= x molar mass

1mass = x .012 kg6.02 10

mass=1.99x10

A

NmassN

xkg

6 1911180 10 1.60 10 2.88 10

1 1x eV x J x J

eV

" #" # =$ %$ %

& '& '

19194 1.60 10 6.40 10

1 1eV x J x J

eV

" #" # =$ %$ %

& '& '

1113

25

7

2.88 10 7.38 10 /3.90 10

7.38 10 /

ex JD x J kgx kg

x MJ kg

= =

=

197

26

6.40 10 3.22 10 /1.99 10

32.2 /

ex JD x J kgx kg

MJ kg

= =

=

IB 12

9

Naturally Occurring Isotopes of Uranium:

1) Uranium-238: most abundant (99.3%) but not used for fuel since it has a very small probability of fissioning when it captures a neutron.

2) Uranium-235: rare (0.3%) but used for fuel since it has a much greater probability of fissioning when captures a neutron but must be a low-energy neutron (thermal neutron).

Fuel Enrichment: process of increasing proportion of uranium-235 in a sample of uranium

Advantage: More uranium is available for fission and a chain reaction can be sustained in a reactor to produce nuclear energy. Disadvantage: If the fuel is enriched to a high level (90% = weapons grade) it can be used in the core of a nuclear weapon. Possession of nuclear weapons is seen by many to be a threat to world peace.

Nuclear Fuel and Reactors

Thermal Neutron: low-energy neutron (1eV) that favors fission reactions energy comparable to gas particles at normal temperatures

1) formation of gaseous uranium (uranium hexafluoride) from uranium ores

2) separated in gas centrifuges by spinning heavier U-238

moves to outside 3) increases proportion of U-235 to about 3-5% of total (low

enrichment) 4) This low enriched hex is compressed and turned into solid

uranium-oxide fuel pellets which are packed into tubes called fuel rods which will be used in the core of a nuclear reactor.

IB 12

10

Fuel Rods: enriched solid uranium

When neutrons are emitted from a fission reaction in the fuel rods, they have a very high kinetic energy and will pass right out of the fuel rod without colliding with another uranium nucleus to cause more fission. High energy neutrons cannot sustain a chain reaction. Therefore, a material is needed to slow them down. Typically, a material like water or graphite (called a moderator) is used to slow down these high-energy neutrons down to thermal levels (thermal neutrons 1 eV) for use in further fission reactions to sustain the chain reaction. The high-energy neutrons slow down when they collide with the atoms in the moderator.

To control the rate at which the thermal energy is produced, and therefore to control the temperature of the reactor core, control rods are used to speed up or slow down the chain reaction. These are rods made of a neutron-absorbing substance, like cadmium or boron. They are inserted in between the fuel rods and raised or lowered as needed. If the reaction is proceeding too fast (too hot) the rods are lowered and enough thermal neutrons are absorbed to slow down the reaction to the desired level. Conversely, if the reaction is too slow, the control rods are raised allowing more thermal neutrons to collide with uranium nuclei.

Chain Reaction neutrons released from one fission reaction go on to initiate further reactions

Uncontrolled Chain Reaction

Controlled Chain Reaction

Uncontrolled nuclear fission: nuclear weapons

Controlled nuclear fission: nuclear power production

1) Some material (control rod) absorbs excess neutrons before they strike another nucleus.

2) This leaves only one neutron from each reaction to produce

another reaction.

3) If the total mass of uranium used is too small, too many neutrons will escape without causing further fissions so the reaction cannot be sustained.

Critical Mass: minimum mass of radioactive fuel (uranium) needed for a chain reaction to occur

The Nuclear Reactor Core

IB 12

11

How is the thermal energy released in the fission reactions used to generate electricity? The coolant (which is often the same as the moderator) is fluid circulating around the fuel rods in the reactor core and is heated up by the thermal energy released in the fission chain reaction. This coolant in a closed loop (primary loop) flows through pipes in a tank of water known as the heat exchanger. Here the thermal energy of the hot coolant is transferred to cooler water in a secondary loop which turns it to steam. This steam expands against fan blades of turbines and turns a magnet is a coil of wire to generate electricity.

2. Sketch a Sankey diagram for a typical nuclear power plant.

1. State the energy transformations in using nuclear fuels to generate electrical energy: Nuclear energy in fuel.thermal energy in coolant . . thermal energy in steam in heat exchangerrotational

mechanical energy/kinetic energyelectrical energy in turbines

IB 12

12

3. Suppose the average power consumption for a household is 500 W per day. Estimate the amount of uranium-235 that would have to undergo fission to supply the household with electrical energy for a year. State some assumptions made in your calculation.

Assume plant is 100% efficient Assume 200 MeV per fission

IB 12

13

4. A fission reaction taking place in a nuclear power station might be:

235 1 141 92 192 0 56 36 03U n Ba Kr n+ + +

Estimate the initial amount of uranium-235 needed to operate a 600 MW reactor for one year assuming 40% efficiency and 200 MeV released for each fission reaction.

IB 12

14

m = m + m

0.19383 u = 180 MeV

23994

1014056

9638

rest mass of 239.052157




Pu un uBa uSr u

=

=

=

=

Plutonium and Nuclear Reactors

Plutonium-239 is another nuclide used as nuclear fuel because of the energy it releases when it undergoes fission. However, it is not as naturally abundant as uranium and so it typically must be artificially produced as a by-product of uranium fission. In a uranium-fueled reactor, as the U-235 depletes over time, the amount of Pu-239 increases. This plutonium is then extracted (by reprocessing of the uranium fuel rods) for use in a plutonium reactor or in a nuclear warhead.

239 1 140 9694 0

1056 38 4Pu n Ba Sr n+ + +

01

238 1 239 23992 0 92 93U n U eNp + ++

239 23993 94

01Np Pu e + +

How is plutonium-239 produced in a uranium reactor? It actually is produced from the non-fissionable isotope uranium-238 that occurs in large amounts in fuel rods. Uranium-238 doesnt undergo nuclear fission but is considered fertile since it produces plutonium-239 by the following process.

Some uranium reactors are even specially designed to produce (or breed) large amounts of plutonium and are known as breeder reactors. They are designed so that the fuel rods are surrounded by a blanket of U-238 so that neutrons escaping from the U-235 fissions will induce the conversion of this U-238 to Pu-239.

1. Complete the nuclear reactions listed above.

3. Determine the amount of energy released in the fissioning of plutonium-239.

2. Construct a nuclear energy level diagram for the series of nuclear reactions listed above.

IB 12

15

Safety Issues and Risks in the Production of Nuclear Power

Thermal Meltdown: Overheating and melting of fuel rods may be caused by a malfunction in the cooling system or the pressure vessel. This overheating may cause the pressure vessel to burst sending radioactive material and steam into atmosphere (as in Chernobyl, Ukraine 1986). Hot material may melt through floor (as in Three Mile Island, Pennsylvania 1979), a scenario dubbed the China syndrome. The damage from these possible accidents is often limited by a containment vessel and a containment building.

Uranium Mining:

open-cast mining: environmental damage, radioactive waste rock (tailings) underground mining: release of radon gas (mines need ventilation), radioactive rock is

dangerous for workers, radioactive waste rock (tailings) leaching: Solvents are pumped underground to dissolve the uranium and then pumped back out.

This leads to contamination of groundwater.

Nuclear Waste:

Low-level waste: Radioactive material from mining, enrichment and operation of a plant must be disposed of. Its often left encased in concrete.

High-level waste: a major problem is the disposal of spent fuel rods. Some isotopes have

lives of thousands of years. Plutoniums is 240,000 years.

1) Some are stored under water at the reactor site for several years to cool off then sealed in steel cylinders and buried underground.

2) Some are reprocessed to remove any plutonium and useful uranium. The remaining

isotopes have shorter lives and the long-term storage need is reduced.

Nuclear Weapons Manufacture:

Enrichment technology could be used to make weapons grade uranium (85%) rather than fuel grade (3%)

Plutonium is most used isotope in nuclear weapons and can be gotten from reprocessing

spent fuel rods

Comparing Nuclear Fuel to Fossil Fuel Advantages:

1. No global warming effect no CO2 emissions 2. Waste quantity is small compared with fossils fuels 3. Higher energy density 4. Larger reserves of uranium than oil

Disadvantages: 1. Storage of radioactive wastes 2. Increased cost over fossil fuel plants 3. Greater risks in an accident (due to

radioactive contamination)

IB 12

16

Nuclear Fusion

Nuclear Fusion: Two light nuclei combine to form a more massive nucleus with the release of energy.

Naturally occurring fusion: main source of Suns energy fusion of hydrogen to helium

1 1 2 01 1 1 11 2 31 1 2

H H H eH H He

+ + +

+ +3 3 4 1 12 2 2 1 1He He He H H+ + +

A probable mechanism for the Suns fusion is called the proton-proton chain.

This chain is sometimes simplified to

4H He energy +

1. If the total mass of four hydrogen nuclei is 6.693 x 10-27 kg and the mass of a helium nucleus is 6.645 x 10-27 kg, determine the energy released in this simplified fusion reaction.

4.3 x 10-12 J

2. The Sun has a radius R of 7.0 x 108 m and emits energy at a rate of 3.9 x 1026 W. The nuclear reactions take place in the spherical core of the Sun of radius 0.25R. Determine the number of nuclear reactions occurring per cubic meter per second in the core of the Sun.

4.1 x 1012 m-3 s-1

IB 12

17

Plasma: The fuel for a fusion reactor is known as a plasma. This is a high energy ionized gas in which the electrons and nuclei are separate. If the energy is high enough (that is, the plasma is hot enough), nuclei can collide fast enough to overcome Coulomb repulsion and fuse together. Heating the plasma to the required temperatures (10 million K) is challenging. The nuclei, since they are charged, are accelerated by means of magnetic fields and forces to high kinetic energies (high temperatures).

Magnetic confinement: These charged particles are contained via magnetic fields and travel in a circle in a doughnut shaped ring called a tokamak which an acronym of the Russian phrase for toroidal chamber with magnetic coils (toroidal'naya kamera s magnitnymi katushkami).

Problems with current fusion technology:

Maintaining and confining these very high-density and high-temperature plasmas for any length of time is very difficult to do.

Experimental reactors that currently can achieve fusion use more energy input than

output which makes them not commercially efficient.

Nuclear fission Nuclear Fusion

Splitting of a heavy nucleus into two or more light nuclei Combination of two light nuclei to form a heavy nucleus

Takes place at room temperature Requires a very high temperature equal to 4 X 106 C

Comparatively less amount of energy is released Enormous amount of energy is released

Fission reaction can be controlled and the energy

released can be used to generate electricity

Fusion reaction cannot be controlled and hence the energy

released cannot be used to generate electricity

It is a chain reaction It is not a chain reaction

It leaves behind radioactive wastes It does not leave behind any radio active wastes

Comparison of Nuclear Fission and Nuclear Fusion

Artificially induced fusion: Attempts have been underway since the 1950s to build fusion reactors. Experimental reactors have come very close to producing more energy than the amount of energy put in, but a commercial fusion reactor has yet to be built.

IB 12

18

Solar Power

Solar heating panel (active solar heater): converts light energy from Sun into thermal energy in water run through it

Photovoltaic cell (solar cell): converts light energy from Sun into electrical energy

Use: heating and hot water Use: electricity

The amount (intensity) of sunlight varies with:

a) time of day b) season (angle of incidence of sunlight altitude of Sun in sky Earths distance from Sun)

c) length of day

d) latitude (thickness of atmosphere)

Which way should a solar panel or cell be facing in the Northern hemisphere? Why? South to receive Maximum radiation from the sun to provide maximum energy for whole day

Advantages:

1. Renewable source of energy 2. Source of energy is free

3. No global warming effect no CO2 emissions

4. No harmful waste products

Disadvantages: 1. Large area needed to collect energy 2. Only provides energy during daylight 3. Amount of energy varies with season,

location and time of day 4. High initial costs to construct/install

Advantages of solar heating panel over solar cell: requires less (storage) area, less cost, more efficient

IB 12

19

1. An active solar heater whose efficiency is 32% is used to heat 1400 kg of water from 200 C to 500 C. The average power received from the Sun in that location is 0.90 kW per m2.

a) How much energy will the solar heater need to provide to heat the water?

b) How much energy will be needed from the Sun to heat the water?

c) Calculate the area of the solar heater necessary to heat the water in 2.0 hours.

2. A photovoltaic cell with an area of 0.40 m2 is placed in a position where the intensity of the Sun is 1.0 kW/m2. a) If the cell is 15% efficient, how much power does it produce?

b) If the potential difference across the cell is 5.0 mV, how much current does it produce?

c) Compare placing 10 of these solar cells in series and in parallel.

IB 12

20

Wind Power

Basic features of a horizontal axis wind turbine: a) Tower to support rotating blades. b) Blades that can be rotated to face into the wind. c) Generator.

d) Storage system or connection to a distribution grid.

Energy transformations: Solar energy heating Earth . . . Kinetic energy of air . . . kinetic energy of turbine . . electrical energy

1. Determine the power delivered by a wind generator:

( )

2

2

2

2

2

3

1/ 2P=

1212121212

KE mvt tmP vtVP vtAdP vt

P v v

P A v

=

" #= $ %& '

" #= $ %& '

" #= $ %& '

=

=

2. Reasons why power formula is an estimate:

a) Not all KE of wind is transformed into mechanical energy

b) Wind speed varies over course of year

c) Density of air varies with temperature

d) Wind not always directed at 900 to blades

3. Why is it impossible to extract this maximum amount of power from the air?

a) Speed of air cannot drop to zero after

impact with blades

b) Frictional losses in generator and turbulence around blades

4. Why are turbines not placed near one another?

a) Less KE available for next turbine b) Turbulence reduces efficiency of next turbine

IB 12

21

1. A wind turbine has a rotor diameter of 40 m and the speed of the wind is 25 m/s on a day when the air density is 1.3 kg/m3. Calculate the power that could be produced if the turbine is 30% efficient.

2. A wind generator is being used to power a solar heater pump. If the power of the solar heater pump is 0.50 kW, the average local wind speed is 8.0 m/s and the average density pf air is 1.1 kg/m3, deduce whether it would be possible to power the pump using the wind generator.

Advantages:




Disadvantages: 1. Large land area needed to collect energy since

many turbines are needed 2. Unreliable since output depends on wind speed

3. Site is noisy and may be considered unsightly 4. Expensive to construct

IB 12

22

Wave Power

Energy can be extracted from water waves in many ways. One such scheme is shown here. Oscillating Water Column (OWC) ocean wave energy converter:

1. Wave capture chamber is set into rock face on land where waves hit the shore.

2. Tidal power forces water into a partially filled

chamber that has air at the top.

3. This air is alternately compressed and decompressed by the oscillating water column.

4. These rushes of air drive a turbine which generates

electrical energy.

Energy transformations: Kinetic energy of water . . . Kinetic energy of air . . . kinetic energy of turbine . . electrical energy

Determining the energy in each wavelength of the wave and the power per unit length of a wavefront

2

Energy in each wavelength of the wave PE = mghPE=mgAPE = ( V)gA

1PE = ( ( ))gA2

1PE = g2

AL

A L

2

2

2

P

1 g2

1 g2

power per unit length1 g2

powerPEt

A LP

T

P A v L

P A vL

=

=

=

=

How would this power estimate change if the waves were modeled as sine waves instead of square waves?

IB 12

23

Advantages:




Disadvantages: 1. Can only be utilized in particular areas 2. High maintenance due to pounding of waves 3. High initial construction costs

2. Waves that are 6.0 meters high with a 100 meter wavelength roll onto a beach at a rate of one wave every 5.0 seconds. Estimate the power of each meter of the wavefront.

1. Waves of amplitude 1.5 meter roll onto a beach with a speed of 10 m/s. Calculate: a) how much power they carry per meter of shoreline

b) the power along a 2 km stretch of beach.

IB 12

24

Hydroelectric Power

A third scheme is called pumped storage. Water is pumped to a high reservoir during the night when the demand, and price, for electricity is low. During hours of peak demand, when the price of electricity is high, the stored water is released to produce electric power. A pumped storage hydroelectric power plant is a net consumer of energy but decreases the price of electricity.

A second scheme, called tidal water storage, takes advantage of big differences between high and low tide levels in bodies of eater such as rivers. A barrage can be built across a river and gates, called sluices, are open to let the high-tide water in and then closed. The water is released at low tide and, as always, the gravitational potential energy is used to drive turbines to produce electrical energy.

There are many schemes for using water to generate electrical energy. But all hydroelectric power schemes have a few things in common. Hydroelectric energy is produced by the force of falling water. The gravitational potential energy of the water is transformed into mechanical energy when the water rushes down the sluice and strikes the rotary blades of turbine. The turbine's rotation spins electromagnets which generate current in stationary coils of wire. Finally, the current is put through a transformer where the voltage is increased for long distance transmission over power lines. By far, the most common scheme for harnessing the original gravitational potential energy is by means of storing water in lakes, either natural or artificial, behind a dam, as illustrated in the top picture at right.

Energy transformations: Gravitational PE of water . . . Kinetic energy of water . . . kinetic energy of turbine . . electrical energy

Advantages:




Disadvantages: 1. Can only be utilized in particular areas 2. Construction of dam may involve land being

buried under water 3. Expensive to construct

IB 12

25

1. A barrage is placed across the mouth of a river at a tidal power station. If the barrage height is 15 meters and water flows through 5 turbines at a rate of 100 kg/s in each turbine, calculate the power that could be produced if the power plant is 70% efficient. 2.6 x 104W

Use average height for EP = mgh

2. A reservoir that is 1.0 km wide and 2.0 km long is held behind a dam. The top of this artificial lake is 100 meters above the river where the water is let out at the base of the dam. The top of the intake is 25 meters below the lakes surface. Assume the density of water is 1000 kg/m3.

a) Calculate the energy stored in the reservoir. 4.3 x 1013 J

b) Calculate the power generated by the water if it flows at a rate of 1.0 m3 per second through the turbine. 875 kW

IB 12

1

Climate Change

Black-body radiation: radiation emitted by a perfect emitter

An object that acts as a black-body will . . . absorb all incoming radiation, not reflect any, then radiate all of it.

Black-Body Radiation

Factors that affect how an object absorbs, emits (radiates), and reflects EM radiation incident on them: 1) Nature of the surface: material, shape, texture, etc.

2) Color:

When the object is in thermal equilibrium with its surroundings,

a) Light-colored or silvery objects: absorb little energy, reflect most energy b) Dark objects: absorb most energy, reflect little energy

energy absorbed = energy radiated Pin = Pout Iin = Iout

When heated, a low-pressure gas will . . .emit a discrete spectrum When heated, a solid will . . . emit a continuous spectrum

1. Not all wavelengths of light will be emitted with equal intensity.

2. Emitted wavelength with highest intensity (max ) is

related to . . . temperature. 3. Area under curve is proportional to . . . total power

radiated by body 4. As body heats up, max . . . decreases

and total power . . . increases

Emission Spectra for Black-Bodies

IB 12

2

Your Turn

Use the axes at right to sketch the emission spectra for a black-body

radiating at low and high temperature. Be sure to label the axes and indicate

which curve represents which temperature.

4

4

4

I TP TAP AT

=

=

=

82 4

where =Stefan-boltzmann constant

=5.67 x 10 Wm K

1. How does the energy radiated by an object change if its temperature doubles?

max 1/T (Wiens law)

The Stefan-Boltzmann Law of Radiation

relates intensity of radiation to the temperature of the body

4

2 16P TT P

2. The supergiant star Betelgeuse has a surface temperature of about 2900 K and a radius of 3 x 1011 m. a) Determine how much energy Betelgeuse radiates each second. 4 x 1030 W

b) What is the intensity of Betelgeuses radiation at its surface?

c) What is the intensity of Betelgeuses radiation at a location that is 3 x 1011 m from its surface?

IB 12

3

d) What major assumption was made in calculating the power radiated by Betelgeuse? That it acts as a black-body

Emissivity (e) ratio of power emitted by an object to the power emitted by a black-body at the same temperature.

3. Calculate the power emitted by a square kilometer of ocean surface at 100C if its emissivity is 0.65.

4

BB

BB

PeP

P ePP e AT

=

=

=

Formula:

e) Compute the power radiated by Betelgeuse if its emissivity is measured to be only 0.90.

4. Calculate the power radiated by the Earth if it is taken to be

a) a black-body at 300 K.

b) at 300 K with an effective emissivity of 0.62.

IB 12

4

1. Calculate the power radiated by the Sun if it is taken to be a black-body at 5778 K and a mean radius of 6.96 x 108 meters.

Solar Radiation

2. What is the intensity of the solar radiation at the Suns surface?

3. What is the intensity of the solar radiation that reaches the upper atmosphere of Earth?

Solar constant: 1360-1370 W/m2 Rounded 1400

See pg. 3 of data booklet for 1.5 x 1011 m

4. How much solar energy is incident on the Earth every second?

Take solar constant and multiply by area of disc as cross-section 1.75 x 1017 W

IB 12

5

8. How much energy is actually absorbed by the Earth each second?

Albedo() ratio of total solar power scattered to total solar power incident

Global annual mean albedo on Earth: 0.30 = 30%

The Earths albedo varies daily and is dependent on:

1. season 2. cloud formations

3. latitude

Meaning: fraction of the total incoming solar radiation that is reflected back out into space

Formula:

total scattered powertotal incident power

reflected

in

PP

=

=

7. Use the diagram at right to determine the Earths average albedo. Atmosphere, clouds, and ground

6. What is the albedo of a black-body? 0 What is the emissivity of a black-body? 1

0.70 x 1.75 x 1017 W = 1.23 x 1017 W

5. What is the average intensity of the solar energy absorbed by the Earth?

Average 1.75 x 1017 W over whole surface area of Earth = 4 pi r2 340 W/m2

IB 12

6

9. Use the results of your prior calculations to estimate the equilibrium temperature of the Earth and comment on your answer.

Assume black-body emiss=1 Pin=Pout Use SB T= 255 k = -18oC too cold

Start to separate Earth into its parts atmosphere vs. ground

10. At present, the average temperature of the Earth is measured to be 288 K.

Actually warmer since atmosphere absorbs some of the radiation emitted by Earth surface

b) Comment on why this might be.

a) Calculate the average emissivity of the Earth.

IB 12

7

Greenhouse Effect a) Short wavelength radiation (visible and short-wave infrared)

received from the Sun causes the Earths surface to warm up. b) Earth will then emit longer wavelength radiation (long-wave

infrared) which is absorbed by some gases in the atmosphere. c) This energy is re-radiated in all directions (scattering). Some is

sent out into space and some is sent back down to the ground and atmosphere.

d) The extra energy re-radiated causes additional warming of the

Earths atmosphere and is known as the Greenhouse Effect.

The Greenhouse Effect

Greenhouse Gases: each has natural and man-made origins

1) Water Vapor (H2O): evaporation 2) Carbon Dioxide (CO2): product of photosynthesis in plants, product of fossil fuel combustion 3) Methane (CH4): product of decay and fermentation and from livestock, component of natural gas

4) Nitrous Oxide (N2O): product of livestock, produced in some manufacturing processes

1. What is the molecular mechanism by which greenhouse gases absorb infrared radiation?

Resonance a transfer of energy in which a system is subject to an oscillating force that matches the natural frequency of the system resulting in a large amplitude of vibration

Application to the greenhouse effect: The natural frequency of oscillation of the molecules of the greenhouse gases is in the infrared region (1 300 m)

2. What do the following transmittance and absorption graphs show about the atmosphere?

Sun radiates in visible Earth radiates in infrared Water vapor absorbs incoming solar radiation and outgoing IR radiation CO2 absorbs outgoing IR radiation

7

IB 12

8

Some energy balance climate models for the Earth

The remaining 70% of the incident energy is absorbed:

51% absorbed by land and water, then emerging in the following ways: o 23% transferred back into the atmosphere as latent heat by the evaporation of water, called

latent heat flux o 7% transferred back into the atmosphere by heated rising air, called Sensible heat flux o 6% radiated directly into space o 15% transferred into the atmosphere by radiation, then reradiated into space

19% absorbed by the atmosphere and clouds, including: o 16% reradiated back into space o 3% transferred to clouds, from where it is radiated back into space

When the Earth is at thermal equilibrium, the same 70% that is absorbed is reradiated:

64% by the clouds and atmosphere 6% by the ground

Outgoing energy

The average albedo (reflectivity) of the Earth is about 0.3, which means that 30% of the incident solar energy is reflected back into space, while 70% is absorbed by the Earth and reradiated as infrared. The planet's albedo varies from month to month, but 0.3 is the average figure. It also varies very strongly spatially: ice sheets have a high albedo, oceans low. The contributions from geothermal and tidal power sources are so small that they are omitted from the following calculations. So 30% of the incident energy is reflected, consisting of:

6% reflected from the atmosphere 20% reflected from clouds 4% reflected from the ground (including land, water and ice)

IB 12

9

Predict increase in planets temp using SB law like test question

IB 12

10

Surface Heat Capacity (CS) energy required to raise the temperature of a unit area of a planets surface by 1 K.

S

S

QCA T

Q AC T

=

=

Formula: Units:

2

Jm K

Temperature change formula: S

S

QCA TP tCA T

=

=

( )

( )

in outS

in out

S

I I tCT

I I tTC

=

=

Surface heat capacity of Earth: CS = 4.0 x 108 J m-2 K-1

2. If the Earth is in thermal equilibrium, it will emit as much radiation as is incident on it from the Sun (344 W/m2). Suppose a change causes the intensity of the radiation emitted by Earth to decrease 10%.

a) Suggest a mechanism by which this might happen.

Increased amounts of greenhouse gases cause more solar radiation to be trapped in atmosphere

b) Calculate the new intensity of radiation emitted by Earth. 0.90(340) = 306 W/m2

c) Calculate the amount by which Earths temperature would rise over the course of a year as a result.

8

( )

(340 306)(365)(24)(3600)4.0 x 10

2.7

in out

S

I I tTC

T

T K

=

=

=

1. How much solar energy is needed to increase the surface temperature of one square kilometer of Earths surface by 2 K?

IB 12

11

Possible models suggested to explain global warming:

1. changes in the composition of greenhouse gases may increases amount of solar radiation trapped in Earths atmosphere

2. increased solar flare activity may increase solar radiation

3. cyclical changes in the Earths orbit may increase solar radiation

4. volcanic activity may increases amount of solar radiation trapped in

Earths atmosphere

In 2007, the IPCC report stated that:

Most of the observed increase in globally averaged temperature since the mid-20th century is very likely due to the increase in anthropogenic [human-caused] greenhouse gas concentrations. (the enhanced greenhouse effect)

Enhanced (Anthropogenic) Greenhouse Effect Human activities have released extra carbon dioxide into the atmosphere, thereby enhancing or amplifying the greenhouse effect. Major cause: the burning/combustion of fossil fuels Possible effect: rise in mean sea-level Outcome: climate change and global warming

Global Warming

Global Warming: records show that the mean temperature of Earth has been increasing in recent years. Global mean surface temperature anomaly

relative to 19611990 In specific terms, an increase of 1 or more Celsius degrees in a period of one hundred to two hundred years would be considered global warming. Over the course of a single century, an increase of even 0.4 degrees Celsius would be significant. The Intergovernmental Panel on Climate Change (IPCC), a group of over 2,500 scientists from countries across the world, convened in Paris in February, 2007 to compare and advance climate research. The scientists determined that the Earth has warmed .6 degrees Celsius between 1901 and 2000. When the timeframe is advanced by five years, from 1906 to 2006, the scientists found that the temperature increase was 0.74 degrees Celsius.

A column of gas and ash rising from Mount Pinatubo in the Philippines on June

12, 1991, just days before the volcanos climactic explosion on June 15.

The global average surface temperature range for each year from 1861 to 2000 is shown by solid red bars, with the confidence range in the data for each

year shown by thin whisker bars. The average change over time is shown by the solid curve.

IB 12

12

2) International Ice Core Research: Between 1987 and 1998, several ice cores were drilled at the Russian Antarctic base at Vostok, the deepest being more than 3600 meters below the surface. Ice core data are unique: every year the ice thaws and then freezes again, forming a new layer. Each layer traps a small quantity of the ambient air, and radioactive isotopic analysis of this trapped air can determine mean temperature variations from the current mean value and carbon dioxide concentrations. The depths of the cores obtained at Vostok means that a data record going back more than 420,000 years has been built up through painstaking analysis.

Inspect the graphical representation of the ice core data and draw a conclusion.

Mechanisms that may increase the rate of global warming

1. Global warming reduces ice and snow cover, which in turn reduces the albedo. This will result in an increase in the overall rate of heat absorption.

2. Temperature increase reduces the solubility of CO2 in the sea and increases atmospheric concentrations.

3. Continued global warming will increase both evaporation and the atmospheres ability to hold water

vapor. Water vapor is a greenhouse gas.

4. The vast stretch of permanently frozen subsoil (permafrost) that stretches across the extreme northern latitudes of North America, Europe, and Asia, also known as tundra, are thawing. This releases a significant amount of trapped CO2.

5. Deforestation results in the release of more CO2 into the atmosphere due to slash-and-burn clearing

techniques, as well as reduces the number of trees available to provide carbon fixation.

1) The Keeling Curve: Named after American climate scientist Charles David Keeling, this tracks changes in the concentration of carbon dioxide (CO2) in Earths atmosphere at a research station on Mauna Loa in Hawaii. Although these concentrations experience small seasonal fluctuations, the overall trend shows that CO2 is increasing in the atmosphere.

Evidence linking global warming to increased levels of greenhouse gases

Smoldering remains of a plot of deforested land in the Amazon rainforest of Brazil. Annually, it is estimated that net global deforestation accounts for about 2 gigatons of carbon emissions to the

atmosphere.

There is a correlation between Antarctic temperature and atmospheric concentrations of CO2

IB 12

13

Coefficient of Volume Expansion () fractional change in volume per degree change in temperature

o

o

VV T

V V T

=

=

Formula: Units:

1K

Rise in Sea-levels

Generally, as the temperature of a liquid rises, it expands. If this is applied to water, then as the average temperature of the oceans increases, they will expand and the mean sea-level will rise. This has already been happening over the last 100 years as the sea level has risen by 20 cm. This has had an effect on island nations and low-lying coastal areas that have become flooded.

Precise predictions regarding the rise in sea-levels are hard to make for such reasons as:

a) Anomalous expansion of water: Unlike many liquids, water does not expand uniformly. From 00C to 40C, it actually contracts and then from 40C upwards it expands. Trying to calculate what happens as different bodies of water expand and contract is very difficult, but most models predict some rise in sea level.

1. The coefficient of volume expansion for water near 20o C is 2 x 10-4 K-1. If a lake is 1 km deep, how much deeper will it become if it heats up by 20o C? 0.4 m

Glaciers on land melting: raise sea level

Sea ice glaciers melting: dont raise sea level

b) Melting of ice: Floating ice, such as the Arctic ice at the North Pole, displaces its own mass of water so when it melts it makes no difference. But melting of the ice caps and glaciers that cover land, such as in Greenland and mountainous regions throughout the world, causes water to run off into the sea and this makes the sea level rise.

IB 12

14

Possible solutions for reducing the enhanced greenhouse effect

1. Greater efficiency of power production.

To produce the same amount of power would require less fuel, resulting in reduced CO2 emissions. 2. Replacing the use of coal and oil with natural gas.

Gas-fired power stations are more efficient (50%) that oil and coal (30%) and produce less CO2.

3. Use of combined heating and power systems (CHP).

Using the excess heat from a power station to heat homes would result in more efficient use of fuel.

4. Increased use of renewable energy sources and nuclear power.

Replacing fossil fuel burning power stations with alternative forms such as wave power, solar power, and wind power would reduce CO2 emissions.

International efforts to reduce the enhanced greenhouse effect

1. Intergovernmental Panel on Climate Change (IPCC): Established in 1988 by the World Meteorological Organization and the United Nations Environment Programme, its mission is not to carry out scientific research. Hundreds of governmental scientific representatives from more than 100 countries regularly assess the up-to-date evidence from international research into global warming and human induced climate change.

5. Use of hybrid vehicles

Cars that run on electricity or a combination of electricity and

gasoline will reduce CO2 emissions.

6. Carbon dioxide capture and storage (carbon fixation)

A different way of reducing greenhouse gases is to remove CO2 from waste gases of power stations and store it underground.

3. Asia-Pacific Partnership of Clean Development and Climate (APPCDC): This is a non-treaty agreement between 6 nations that account for 50% of the greenhouse emissions (Australia, China, India, Japan, Republic of Korea, and the United States.) The countries involved agreed to cooperate on the development and transfer of technology with the aim of reducing greenhouse emissions.

2. Kyoto Protocol: This is an amendment to the United Nations Framework Convention on Climate Change. In 1997, the Kyoto Protocol was open for signature. Countries ratifying the treaty committed to reduce their greenhouse gases by given percentages. Although over 177 countries have ratified the protocol by 2007, some significant industrialized nations have not signed, including the United States and Australia. Some other countries such as India and China, which have ratified the protocol, are not currently required to reduce their carbon emissions.

Documents

Topic 8 Energy Power and Climate Change