msolfmancom.files.wordpress.com · web viewmar 04, 2021 · consider an internal combustion...

Physics 42S IBTopic 8 – Energy Production

Physics 42S IBMiles Macdonell Collegiate

8.1 – Energy sources

Nature of science:

Risks and problem-solving: Since early times mankind understood the vital role of harnessing energy and large-scale production of electricity has impacted all levels of society. Processes where energy is transformed require holistic approaches that involve many areas of knowledge. Research and development of alternative energy sources has lacked support in some countries for economic and political reasons. Scientists, however, have continued to collaborate and share new technologies that can reduce our dependence on non-renewable energy sources. (4.8)

Understandings:

Specific energy and energy density of fuel sources

Sankey diagrams Primary energy sources Electricity as a secondary and versatile form

of energy Renewable and non-renewable energy

sources

Applications and skills:

Solving specific energy and energy density problems

Sketching and interpreting Sankey diagrams Describing the basic features of fossil fuel

power stations, nuclear power stations, wind generators, pumped storage hydroelectric systems and solar power cells

Solving problems relevant to energy transformations in the context of these generating systems

Guidance:

Specific energy has units of J kg–1; energy density has units of J m–3

The description of the basic features of nuclear power stations must include the use of control rods, moderators and heat exchangers

Derivation of the wind generator equation is not required but an awareness of relevant assumptions and limitations is required

Students are expected to be aware of new and developing technologies which may become important during the life of this guide

International-mindedness:

The production of energy from fossil fuels has a clear impact on the world we live in and therefore involves global thinking. The geographic concentrations of fossil fuels have led to political conflict and economic inequalities. The production of energy through alternative energy resources demands new levels of international collaboration.

Theory of knowledge:

The use of nuclear energy inspires a range of emotional responses from scientists and society. How can accurate scientific risk assessment be undertaken in emotionally charged areas?

Utilization:

Generators for electrical production and engines for motion have revolutionized the world (see Physics sub-topics 5.4 and 11.2)

The engineering behind alternative energy sources is influenced by different areas of physics (see Physics sub-topics 3.2, 5.4 and B.2)

Energy density (see Chemistry sub-topic C.1) Carbon recycling (see Biology sub-topic 4.3)

- 1 -

Topic 8 Energy Production

Data Booklet Reference:

Power= energytime

Power=12Aρ v3

Aims:

Aim 4: the production of power involves many different scientific disciplines and requires the evaluation and synthesis of scientific information

Aim 8: the production of energy has wide economic, environmental, moral and ethical dimensions

- 2 -


Energy Density

The energy density of a fuel is the energy that can be obtained from a unit volume for that fuel. Energy density is measured inJ m−3. Specific energy is the energy that can be obtained from a unit mass of that fuel. Specific energy is measured inJ k g−1.

For fossil fuels this is simply the heat of combustion whereas for nuclear power mass is converted directly in to energy through Einstein’s energy equationE=mc2 (see Topic 7 - Nuclear Physics).

Fuel Specific EnergyES/J k g

−1Energy DensityED/ J m

−3

Hydrogen 1.4×108 1.0×107

Coal 3.2×107 7.2×1010

Natural Gas 5.4×107 3.6×107

Diesel Oil 4.6×107 3.7×1010

Kerosene 4.3×107 3.3×1010

Gasoline 4.6×107 3.4×1010

Uranium 7.6×1013 1.3×1018

- 3 -


Example 1

Show that the energy density can be calculated by the following equation:

ED=ρES

Example 2

Use the preceding table to estimate the density of Uranium.

- 4 -


Energy Degradation and Power Generation

Thermal energy may be completely converted to work in a single process, but the continuous conversion of this energy into work requires a cyclical process and a transfer of some energy from the system (lost energy).

Energy, while always being conserved, becomes less useful, i.e. it cannot be used to perform mechanical work. This is called energy degradation.

Sankey Diagrams

Consider an internal combustion engine. These engines typical have an efficiency of25%. If the internal combustion process produces800 J of energy,200 J can do work while600 J is degraded. We can represent this with a Sankey Diagram.

Sankey Diagrams show the flow of energy from one system to another. The width of each arrow in the diagram is proportional to the energy carried by that arrow. The arrow that continues forward shows the useful energy, whereas the arrows that branch of show the degraded or lost energy.

- 5 -

600 J

200 J

800 J


Example 1

A Sankey diagram for the generation of electrical energy using fossil fuel as the primary energy source is shown.

Use the Sankey diagram to estimate the efficiency of production of electrical energy and explain your answer.

Example 2

The most efficient coal power plant has an efficiency of40%. Use the grid below to draw a Sankey diagram to represent the energy loss, the useful work done, and total energy if the useful energy produced is12.0MJ .

- 6 -


World Energy Sources

As civilizations developed, the demand for power increased. In the ancient era, people used roughly8MJ per day ( 92W per person) for food and other energy needs. In the modern era, the need for energy has increased to a global average of300MJ per day ( 3.5kW per person). In North America and Western Europe, this value is approximately14 kW per person and7kW per person respectively, with the northern countries using up to18kW per person, whereas parts of Africa and the Middle East use less than0.1kW per person.

The sources of energy can be classified as non-renewable or renewable.

Non-renewable sources are finite sources, which are being depleted, and will run out. The energy stored in these sources is, in general, a form of potential energy, which can be released by human action.

Renewable sources are infinite (relatively) sources of energy. They will not be depleted. These energy sources are doing work every day humans can harness this energy. Most of these sources are directly or indirectly related to the Sun.

Non-Renewable Sources Renewable SourcesFossil Fuels

Coal Oil Natural Gas

Nuclear Fuels Uranium

Hydroelectric and Tidal EnergyWind EnergyWave EnergySolar Energy

Energy Production and the Percentage of the Total Energy ProductionFuel Percentage of total energy

production(% )Carbon Dioxide emission(gM J−1 )

Oil 32 70Natural Gas 21 50Coal 27 90Nuclear 6 −¿Hydroelectric 2 −¿Biofuels 10 variableOthers (solar, wind, waves) ¿2 −¿

Fossil fuels make up80% of all the worlds energy production, but also have a large carbon footprint. Other energy sources have a small or no carbon footprint by comparison, but either has lower power output or other concerns.

- 7 -


Electricity Production

We are very dependent on electricity, and many energy sources that are available today produce electricity. The production of electricity takes place in a generator. A generator uses mechanical energy to rotate a coil in a magnetic field (see Topic 11 – Electromagnetic Induction). The generator converts mechanical energy to electrical energy.

The preceding flowchart shows that all energy sources (except photovoltaic cells) use mechanical energy (kinetic energy) as a mediator to produce electrical energy through electromagnetic induction.

Fossil Fuel Power Production

Oil, Coal, and Natural gas have been produced over millions of years. They are produced by the decomposition of buried organic matter by bacteria and under high pressure from the materials on top. As the world industrialized, the need for power increased. Industries tended to develop around abundant sources of fossil fuels. Developing countries rely heavily on less efficient and more polluting fossil fuels as their energy demands increase exponentially.

The efficiency of fossil fuel power plants varies depending on the type of fossil fuel being used. Coal burning power plants typically have an efficiency of30% depending on the technology level of the plant. Coal plants have achieved an efficiency of46%, but these are newer plants and are very rare. Whereas natural gas power plants have an efficiency of42%. The newer power plants with advanced technology can achieve efficiencies of up to49%, but again these are rare, not the standard.

- 8 -

generator

kinetic energy of particles

nuclear power

electrical energy

kinetic energy of rotation

thermal energy

solar(photovoltaic cells)

wind energy

hydroelectric

wave energy

fossil fuels


Fossil Fuel Mining

Coal is obtained by mining. The mining process produces many toxic substances, and the coal itself is high is sulphur content and heavy metals. Rain can wash away the sulphur and heavy metals. This creates serious environmental problems if the acidic run off enters water reserves. Coal mining sites are also considered environmental disaster areas. Many countries have strict laws requiring mining companies to have a plan for reclaiming the area after the mining is over.

Drilling for oil and natural gas also has adverse environmental effects. Many accidents lead to leakage of oil at sea and on land.

Example 1

Determine the efficiency of the coal power plant by interpreting the following Sankey diagram. Identify the sources and the percent energy loss at each step by using the above image of the coal powerplant.

- 9 -


Example 2

A power plant produces electricity by burning coal, using the thermal energy produced as input to a steam engine, which will make a turbine turn, producing electricity. The plant has a power output of400MW and operates at an overall efficiency of35%.

(a) Calculate the rate at which thermal energy is being provided by the burning coal.

(b) Calculate the rate that the coal is being burned if the coal has an energy density of30MJ k g−1.

(c) The thermal energy discarded by the power plant is removed by water. The temperature of the water must not increase more than5℃. Calculate the rate at which the water must flow.

Advantages of Fossil Fuels Disadvantages of Fossil Fuels Relatively cheap (while they last) High power output (high energy

density) Variety of engines and devices use

them directly and easily Extensive distribution networks are

already in place

Will run out Pollute the environment (extraction

and use) Contribute to the greenhouse effect

- 10 -


- 11 -


Example 3

The following data are available for a natural gas power station that has a high efficiency.

Rate of consumption of natural gas ¿14.6 kg s–1

Specific energy of natural gas ¿55.5MJk g–1

Efficiency of electrical power generation ¿59.0%Mass ofCO2 generated perkg of natural gas ¿2.75 kgOne year ¿3.16×107 s

(a) Calculate, with a suitable unit, the electrical power output of the power station.

(b) Calculate the mass of CO2 generated in a year assuming the power station operates continuously.

(c) Explain, using your answer to (b), why countries are being asked to decrease their dependence on fossil fuels.

(d) Describe, in terms of energy transfers, how thermal energy of the burning gas becomes electrical energy.

- 12 -


Nuclear Power

Nuclear reactors use Uranium-235 to produce energy. Natural sources of uranium most commonly have Uranium-238, and only about0.7% is Uranium-235. The uranium must be enriched to contain enough fissionable material to be used in nuclear reactors, usually3% or higher. The uranium is enriched and processed into fuel rods (tubes containing uranium).

n01 + U92

235 → U92236 → Xe54

140 + Sr3894 +2 n0

1

The extra neutrons released can initiate further nuclear reactions which release more neutrons. This reaction is self-sustaining and is called a chain reaction. For a chain reaction to occur, enough Uranium-235 must be present, otherwise the neutrons escape without causing further reactions – this minimum mass of uranium is called the critical mass. Uranium-235 will only capture neutrons that move at low energies(≈1eV ). The neutrons will slow down from successive collisions with the moderator, a material surrounding the fuel rods. The rate of reaction is determined by the number of neutrons available to be captured by the uranium. Too few neutrons will result in the reaction stopping altogether. Too many neutrons will result in an uncontrollably large release of energy.

Control rods are used to absorb excess neutrons to ensure that the reactions continue at a self-sustaining rate, while not resulting in uncontrolled nuclear reaction (as in nuclear weapons).

- 13 -


Plutonium Production

The fast neutrons can be used to bombard Uranium – 238. When bombarded with neutrons, Uranium – 238 undergoes a series of beta decay and produces plutonium.

n01 + U92

238 → U92239

U92239 → Np93

239 + e−10 + ν0

0

Np93239 → Pu94

239 + e−10 + ν0

0

Uranium – 238 is a non-fissionable element. This process produces a fissionable material that can be used in other nuclear reactors, but it can also be used as nuclear weapons.

- 14 -

A schematic diagram of a heavy water fission reactor.

steamgenerator

steam

water

pump

coolant(pressurized heavy water)

fuel rods

control rods (can be raised or lowered)


Safety Concerns

Thermonuclear Meltdowns

One of the greatest safety concerns of Nuclear power is the risk of thermonuclear meltdown. If the heat is uncontrolled, the fuel rods can begin to melt. When the core melts, the control rods are ineffective on the removal of the excess neutrons and the chain reaction continues uninhibited.

Nuclear Waste

The products of nuclear fission are radioactive. Disposal of these materials, at present, is by burying them very deep in sealed containers to avoid leaks. Some of the waste material can be used in low level nuclear reaction, but the energy output is significantly lower. There is no real long-term solution to this problem.

Uranium Mining

Like all forms of mining, uranium mining is very dangerous. In addition to the common mining dangers, radioactive decay of uranium produces radon gas, a known carcinogen. Also, uranium is radioactive. Radioactivity is a hazard to human health.

Nuclear Weapons

As mentioned earlier, the fuel and products of nuclear fission can be used to make nuclear weapons. This can cause geopolitical tension and is the main reason nuclear power plants are not in operation in developing countries.

- 15 -

Advantages of Nuclear Power Disadvantages of Nuclear Power High power output Large reserves of nuclear fuel Clean, without carbon emissions

Difficult to dispose of radioactive waste products

Major public health hazard should a reactor meltdown occur

Health risks involved in mining and extraction of uranium

Nuclear reactors can produce material used in nuclear weapons


Nuclear Fusion

H12 + H1

3 → He24 + n0

1 +17.6MeV

Deuterium and tritium can undergo nuclear fusion to produce helium, a neutron and energy. Deuterium can be isolated from electrolysis of heavy water and tritium can be produced by the bombardment of lithium with neutrons.

To cause the fusion of two elements, the positively charged nuclei need to be brought close enough for the nuclear forces to cause these reactions. This requires a very high temperature(108 K ) so the nuclei will have enough kinetic energy to get this close. At this temperature the hydrogen isotopes are ionized and become plasma. The plasma is contained in a tokamak, a magnetic chamber that allows the plasma to move around without touching the container itself. If the plasma were to touch the container, it would transfer thermal energy to the container (probably melting it) and the plasma will condense back into a gas.

The energy supplied to produce a fusion reaction (to convert deuterium and tritium into plasma and to contain it) is greater than the energy produced by the reaction. At this point, it is not a viable option for nuclear power.

Fusion has a lot of potential for a world energy source. The fuel for fusion reactions is plentiful, it does not produce radioactive waste, and the products cannot be used for nuclear weapons.

Example 1

As discussed in Subtopic 7.2, 1.0kg of uranium-235 releases a quantity of energy equal to70×1012 J . Natural uranium (mainly uranium-238) contains about0.70% of uranium-235 (by mass). Calculate the specific energy of natural uranium.

- 16 -


Example 2

The following fission reaction takes place in a nuclear reactor.

(a) Calculate the energy released by the fission of one atom of uranium.

n01 + U92

235 → U92236 → Ba56

141 + Kr3692 +3 n0

1 U92235 =235.043923 u; Ba56

141 =140.914411u;

Kr3692 =91.926156u

(b) Calculate the mass of uranium needed to produce1.37GW in one day (the approximate power needs of Winnipeg).

Example 3

A nuclear power plant produces800MWof electrical power with an overall efficiency of 35%. The energy released in the fission of one nucleus of uranium-235 is170MeV . Estimate the mass of uranium used per year.

- 17 -


Hydroelectric

The energy used to produce electricity in hydroelectric dams is the work done by the gravitational force.

power=mght

As the water flows through the turbines, the water flows from a high gravitational potential to a low gravitational potential. The work done by gravity turns the turbines and mechanical energy is used to turn a generator.

The above formula is an oversimplification. The mass of water is not easy to measure directly. The actual formula uses the density and volume flow rate of the water.

The mass that flows through the dam is equal to the product of the density of the water and the volume of water.

power= ρ∆Vght

power=ρ ∆Vtgh

power=ρQgh

ρ is the density of water(1.00×103 kg m−3 ) andQ is the volume flow rate of water (measured inm3 s−1; 1m3=103L).

The water can be stored in lakes where the height of the lake is kept at a maximum to maximize the work done by gravity. These lakes can be human made by damming up a river or by damming up a river mouth of natural lakes.

Tidal water can be stored and released through a dam. As high tide comes in twice a day, the water could be stored behind floodgates and then released through a turbine as low tide occurs. This is one of the few renewable sources of energy that has nothing to do with the Sun. The Moon’s gravitational pull on the Earth causes the tides.

Pump storage systems can also be used; however, more energy is expended than gained. However, if the energy is being supplied by another source, the pump storage can be used to save the water for times when energy demand is high.

- 18 -


Example 1

Find the power developed when water in a stream flows with a flow rate of50 Ls−1 falls a height of15m.

Example 2

In a pumped storage hydroelectric system, water is stored in a dam of depth34m.

The water leaving the upper lake descends a vertical distance of110m and turns the turbine of a generator before exiting into the lower lake.

- 19 -


Water flows out of the upper lake at a rate of 1.2×105m3 per minute. The density of water is1.0×103 kgm –3.

(a) Estimate the specific energy of water in this storage system, giving an appropriate unit for your answer.

(b) Show that the average rate at which the gravitational potential energy of the water decreases is2.5GW .

(c) The storage system produces1.8GWof electrical power. Determine the overall efficiency of the storage system.

(d) After the upper lake is emptied it must be refilled with water from the lower lake and this requires energy. Suggest how the operators of this storage system can still make a profit.

Advantages of Hydroelectric Energy Disadvantages of Hydroelectric Energy Source is the water flow, so it’s ‘Free’ Inexhaustible Clean, without carbon emissions

Very dependent on location Requires drastic change to

environment Initial cost is high

- 20 -


Wind Power

To calculate the power produced by a wind turbine, we use the kinetic energy of the wind:

EK=12mv2

The mass of the air can be determined by using the density of air and an approximate shape of the air. The air traveling through the turbine is roughly a cylinder.

E=12ρ∙∆V ∙v2

E=12ρ∙ A ∙ v ∆ t ∙ v2

E=12ρ∙ A ∙ v3∆t

E∆ t

=12ρ∙ A ∙ v3

P=12ρA v3

power=12Aρ v3

Where,

power is the amount of energy, in joules( J ) produced per second in watts(W ).

A is the area spanned by the blades of the wind turbine inm2.

ρ is the density of air, usually1.2kgm−3.

v is the speed of the wind inms−1.

- 21 -

Av

v ∆t


This formula assumes that all the kinetic energy of the wind is transferred to the turbine. This is impossible because the wind would have to stop after it passes through the turbine.

For effective use of this technology, wind speeds between6ms−1 to14ms−1 are needed

Advantages of Wind Power Disadvantages of Wind Power Source is the wind, so it’s ‘Free’ For practical purposes it is

Inexhaustible Clean, without carbon emissions Ideal for remote locations

Not dependable – only works if there is wind

Very dependent on location, best locations are far from cities, more power loss

Low power output Noisy Maintenance cost is high

Example 1

Calculate the power per unit area of the energy produced by wind turbines with a wind speed of12.0ms−1. Assume the density of air isρ=1.2kg m−3.

What is the power produced if a wind turbine with25m blades?

- 22 -


Example 2

What is the speed of the wind where a wind turbine produces5.75GJ of energy in a24h period with blades35m long?

Example 3

Calculate the number of windmills that are needed to supply power to a small village whose power needs are5.0MW . Each windmill has a blade diameter12m, the density of air is1.2kgm−3

and the wind speed is8.0ms−1.

- 23 -


This question is about energy sources.

A small island is situated in the Arctic. The islanders require an electricity supply but have no fossil fuels on the island. It is suggested that wind generators should be used in combination with power stations using either oil or nuclear fuel.

(a) Suggest the conditions that would make use of wind generators in combination with either oil or nuclear fuel suitable for the islanders.

(b) Conventional horizontal-axis wind generators have blades of length4.7m. The average wind speed on the island is7.0ms−1 and the average air density is1.29 kgm−3.

(i) Deduce the total energy, inGJ , generated by the wind generators in one year.

(ii) Explain why less energy can actually be generated by the wind generators than the value you deduced in (b)(i).

- 24 -


(c) The energy flow diagram (Sankey diagram) below is for an oil-fired power station that the islanders might use.

(i) Determine the efficiency of the power station.

(ii) Explain why energy is wasted in the power station.

(iii) The Sankey diagram in (c) indicates that some energy is lost in transmission. Explain how this loss occurs.

(d)

- 25 -


Solar Power

Active Solar Devices

Early applications of solar power were used to heat water and air in blackened reservoirs or pipes to heat houses. There is a reflective surface underneath the pipes to increase the amount of energy absorbed.

More sophisticated devices using parabolic mirrors to collect and focus more solar radiation can be used to heat water to much higher temperatures(500℃−2000℃ ). The steam produced can turn turbines to produce electrical energy.

Photovoltaic Cells

A photovoltaic cell converts solar energy directly into a direct current. The photovoltaic effect is directly related to the photoelectric effect (see Topic 12 – Quantum Physics) but it is a slightly different process. The actual working of photovoltaic cells depends on the physics of semiconductors.

- 26 -

reflecting surface blackened pipes

cold water in

warm water out

sunlight


When sunlight hits a photovoltaic cell, a potential difference is established based on the energy of the photons absorbed by the electrons from the valence band which transition to the conduction band of the semiconductor and become free. The electrons in the conduction band diffuse a spread out along the conduction band. When they reach a junction where they are then accelerated through a built in potential difference and generate EMF.

The biggest difference between the photoelectric effect and the photovoltaic effect is that in the photoelectric effect the electrons ejected have high threshold energies to overcome to cross the vacuum to reach the other electrode.

In photovoltaic cells, the semiconductors are in contact (more or less) and the energy required to cross from the valence band to the conduction band is very low( 1eV ).

Example

The average intensity of solar radiation incident on the Earth surface is245Wm−2. In an array of photovoltaic cells, solar energy is converted to electrical energy with an efficiency of20%. Estimate the area of photovoltaic cells needed to provide2.5kW of electrical power.

- 27 -

electronEnergy level diagram for a silicon semiconductor.

energy

1eV

conduction band

valence band

gap


8.2 – Thermal energy transfer

Nature of science:

Simple and complex modelling: The kinetic theory of gases is a simple mathematical model that produces a good approximation of the behaviour of real gases. Scientists are also attempting to model the Earth’s climate, which is a far more complex system. Advances in data availability and the ability to include more processes in the models together with continued testing and scientific debate on the various models will improve the ability to predict climate change more accurately. (1.12)

Understandings:

Conduction, convection and thermal radiation

Black-body radiation Albedo and emissivity The solar constant The greenhouse effect Energy balance in the Earth surface–

atmosphere system

Applications and skills:

Sketching and interpreting graphs showing the variation of intensity with wavelength for bodies emitting thermal radiation at different temperatures

Solving problems involving the Stefan–Boltzmann law and Wien’s displacement law

Describing the effects of the Earth’s atmosphere on the mean surface temperature

Solving problems involving albedo, emissivity, solar constant and the Earth’s average temperature

International-mindedness:

The concern over the possible impact of climate change has resulted in an abundance of international press coverage, many political discussions within and between nations, and the consideration of people, corporations, and the environment when deciding on future plans for our planet. IB graduates should be aware of the science behind many of these scenarios.

Theory of knowledge:

The debate about global warming illustrates the difficulties that arise when scientists cannot always agree on the interpretation of the data, especially as the solution would involve large-scale action through international government cooperation. When scientists disagree, how do we decide between competing theories?

Utilization:

Climate models and the variation in detail/processes included

Environmental chemistry (see Chemistry option topic C)

Climate change (see Biology sub-topic 4.4 and Environmental systems and societies topics 5 and 6)

The normal distribution curve is explored in Mathematical studies SL sub-topic 4.1

- 28 -


Guidance:

Discussion of conduction and convection will be qualitative only

Discussion of conduction is limited to intermolecular and electron collisions

Discussion of convection is limited to simple gas or liquid transfer via density differences

The absorption of infrared radiation by greenhouse gases should be described in terms of the molecular energy levels and the subsequent emission of radiation in all directions

The greenhouse gases to be considered are CH4, H2O, CO2 and N2O. It is sufficient for students to know that each has both natural and man-made origins.

Earth’s albedo varies daily and is dependent on season (cloud formations) and latitude. The global annual mean albedo will be taken to be 0.3 (30%) for Earth.

Data Booklet Reference:

P=eσAT 4

λmax (metres )=2.90×10−3

T (Kelvin )

I= powerA

albedo= total scattered powertotal incident power

Aims:

Aim 4: this topic gives students the opportunity to understand the wide range of scientific analysis behind climate change issues

Aim 6: simulations of energy exchange in the Earth surface–atmosphere system

Aim 8: while science has the ability to analyse and possibly help solve climate change issues, students should be aware of the impact of science on the initiation of conditions that allowed climate change due to human contributions to occur. Students should also be aware of the way science can be used to promote the interests of one side of the debate on climate change (or, conversely, to hinder debate).

- 29 -


The Solar Constant

The power per unit area received at point from the sun is called the intensityI , so,

I= powerA

Where,

power is the amount of energy produced per second in watts(W ) by the sun.

A is the area of the sphere of our orbit (approximating a circular orbit).A=4 π r2

And r is the radius of our orbit(1 A .U .=1.50×1011m)

I is the intensity of the sunlight received by one meter squared at the surface of our outer atmosphere. This is about1.36×103Wm−2. This is known as the solar constant for the Earth.

Example

Calculate the power output of the sun.

Calculate the intensity of the sun at the surface of the sun.

(rs=6.96×108m)

- 30 -


This number varies±1.5% due to changes in the power output of the Sun and by±4.0% due to the variation of our distance from the Sun due to our orbit being elliptical.

The total amount of energy received by one squared meter per day is called the daily insolation. The daily insolation varies throughout the year.

The following graph gives the daily isolation for the northern hemisphere.

- 31 -

at60 ° lattitude

at36 ° lattitude

June

insolation/MJm−2da y−1

30

20

10

0

MayAprilMarchFebruary January December November October September August July June


The cause of the largest variation of solar energy received by any one point on the Earth is due to our axial tilt. At higher latitudes, the length of day is shorter; the angle of incidence of the solar rays is greater and1400W is spread over a larger area. In addition, the solar energy has to go through a greater more atmosphere, so more energy will be absorbed before it reaches the surface.

Advantages of Solar Power Disadvantages of Solar Power Source is the Sun, so it’s ‘Free’ Inexhaustible Clean

Works during the day only Affected by cloudy weather Low power output Requires large areas Initial cost is high

Albedo

The albedo of a body is defined as the ratio of the power of the radiation reflected or scattered from the body to the total radiation incident on the body.

albedo= total scattered powertotal incident power

- 32 -

southpole

solar radiation

northpole

atmosphere

earth

equator


Albedo is a unit-less value. The global average albedo is about0.3. This varies region to region and it varies at different time of the year, depending on cloud cover, snowfall and angle of the sun. Typically, the lighter something is, the higher the albedo and the darker something is, the lower the albedo.

Surface AlbedoSnow 0.85Ocean ice 0.60Sand 0.4Green grass 0.25Soil 0.17Deciduous forest 0.15−0.18Coniferous forest 0.09−0.15Charcoal 0.04

Water is an interesting substance with respect to albedo. The angle of incidence determines the albedo of water. When the incident angle from the normal is low (the sun is directly overhead), the albedo of water is also low. When the incident angle from the normal is high (the sunlight hits the water at an angle), the albedo of water is high.

Example 1

The diagram shows an energy balance climate model for a planet.

The intensities of the reflected and radiated radiation are given in terms of the incident intensity II. Determine the emissivity and albedo of this planet.

- 33 -


The Stefan-Boltzmann Law

All bodies at an absolute temperatureT (in kelvin) radiate energy in the form of electromagnetic waves. The power radiated by a body is governed by the Stefan-Boltzmann Law.

The amount of energy per second (i.e. the power) radiated by a body it determined by the following formula:

power=eσAT 4

Where,

power is the amount of energy radiated per second in watts(W ) by the body.

e is the emissivity of the surface.

σ is the Stefan-Boltzmann constant; σ=5.67×10−8Wm−2 K−4

A is the surface area of the of the body.

T is the absolute temperature of the object, in kelvin(K )The emissivity of a substance varies from0−1. The special casee=1 corresponds to what is called a black body, a theoretical body that is a perfect emitter. Emissivity is the ratio of energy/power emitted (per unit area) of a body to the energy/power emitted (per unit area) of a black body of the same dimensions at the same temperature.

Black Body Radiation

power=σAT 4

Surface EmissivityBlack Body 1Ocean water 0.8Ice 0.1Dry land 0.7Land with vegetation 0.6

- 34 -


Example 2

The Sun has a radius of7.0×108mand is a distance1.5×1011mfrom Earth. The surface temperature of the Sun is5800 K.

(a) Show that the intensity of the solar radiation incident on the upper atmosphere of the Earth is approximately1400Wm−2.

(b) The albedo of the atmosphere is 0.30. Deduce that the average intensity over the entire surface of the Earth is245W m−2.

(c) Estimate the average surface temperature of the Earth.

- 35 -


Wien’s Law

The energy radiated from a body as electromagnetic radiation is distributed over an infinite range of wavelengths. However, most of the energy is radiated at a specific wavelength determined by the temperature of the body.

Since the peak wavelength is dependent on temperature, we can determine the relationship between the two. This is given by Wien’s Law:

λT=2.90×10−3m K

The surface of the earth has an average temperature of15℃. Calculate the peak wavelength emitted by the earth.

The surface of the sun has an average temperature of5800K . Calculate the peak wavelength emitted by the sun.

The human body has an average temperature of37℃. Calculate the peak wavelength emitted by a human body.

- 36 -

For different temperatures, the peak wavelength of the radiation occurs at specific wavelengths that vary with temperature. Higher temperature means a shorter wavelength.

273K

300K

350K

3.02.52.01.51.00.5

0.2

0.4

0.6

0.8

1.0

λ /×10−5m

I


The emissivity of a body is a ratio of the amount of energy radiated by a body compared to black body radiation. Dark and dull materials have e close to1, whereas white and shiny surfaces haveeclose to0. The emissivity of an object also gives the ratio to which a body will absorb energy compared to that of a black body.

Example 1

What is the power emitted by a black body with a surface area of5.0m2 at a temperature of30℃?

- 37 -

For the same temperatures, the peak wavelength emitted is the same; however, the intensity is dependent on the emissivity of the surface.

0.25

0.80

1.00

3.02.52.01.51.00.5

0.2

0.4

0.6

0.8

1.0

λ /×10−5m

I


Example 2

What is the temperature of12.0m2of ocean water that over a25minute period emits5.77×106 J of energy?

Example 3

By what factor does the power emitted by a body increase when the temperature is increased from100℃ to200℃?

A body at temperatureT 1 will radiate power at a ratePout=eσAT 14, but will also absorb energy

from its surroundings atT 2 at a rate ofP¿=eσAT 24. The net power lost by the body is:

Pnet=Pout−P ¿

Pnet=eσAT 14−eσAT 2

4

Pnet=eσA (T14−T 24 )

Example 4

The emissivity of the human body is approximatelye=0.90. Assuming a body temperature of37℃ and a body surface area of1.60m2, calculate the total amount of energy lost by the body when exposed to0℃ for30minutes.

- 38 -


The Greenhouse Effect

The greenhouse effect is the warming of the earth caused by infrared radiation, emitted by the earth’s surface, which is absorbed by various gases in the atmosphere and then partly reradiated back towards the surface.

The gases primarily responsible for this absorption (the greenhouse gases) are water vapour, carbon dioxide, methane and nitrous oxide.

Greenhouse gas Natural sources Anthropogenic sourcesH 2O (water vapour) evaporation of water from oceans,

rivers and lakesCO2(carbon dioxide) forest fires; volcanic eruptions;

evaporation of water from oceansburning fossil fuels in power plants and cars; and burning forests

C H 4 (methane) wetlands, oceans, lakes and rivers flooded rice fields; farm animals; processing of coal, natural gas and oil; burning biomass

N2O (dinitrogen monoxide, nitrous oxide)

forests; oceans; soil; grasslands burning fossil fuels; manufacture of cement; fertilizers; deforestation (reduction of nitrogen fixation in plants)

Energy Balance (see handout)

Table 1 – Energy balance for the entire Earth system.

Mechanism Intensity in (arbitrary Units)

Radiation from the Sun 100Total Energy for the entire Earth system 100Mechanism Intensity out (arbitrary

Units)Reflected from the surface 5Reflected from the atmosphere 25Radiation from clouds and atmosphere 65Radiation from the surface with no atmospheric absorption (the IR window)

5

Total Energy for the entire Earth system 100

- 39 -


Table 2 – Energy balance for the Earth’s surface.

Mechanism Intensity in (arbitrary Units)

Transmitted to the surface from the Sun 50Absorbed Infra-red radiation re-radiated back to the Earth (greenhouse effect)

96

Total Energy for the Earth surface 146Mechanism Intensity out (arbitrary

Units)Reflected from the surface 5Convection and evaporation 30Infra-red radiation from the surface 106Radiation from the surface with no atmospheric absorption (the IR window)

5

Total Energy for the entire Earth surface 146

Mechanism for Photon Absorption

A molecule of carbon dioxide will absorb a photon in the same way that an electron will absorb a photon of a certain energy level. The same effect of photon absorbed by molecules is observed as that of electrons (discrete, quantized energy levels; see Topic 12 – Quantum and Nuclear Physics) however this energy is vibrational and rotational. The vibrational and rotational energy absorbed by carbon dioxide resides in the infrared spectrum of photons, at approximately the same energy as the infrared photons emitted by the earth.

Photons emitted from the earth that pass through these gases will be absorbed. The molecules will transition quickly from a low energy state to a high energy state and return to their lower energy state by re-emitting the infrared photon. The exact process is a quantum mechanical concept; however, it is shown that the carbon dioxide molecules resonate at a natural frequency in the infrared spectrum.

The infrared photons absorbed by the carbon dioxide molecules are re-emitted in all directions. Some of the energy is released into space, but some is released back at the Earth which heats the Earth and the atmosphere. This energy is essentially trapped in the atmosphere.

- 40 -

msolfmancom.files.wordpress.com · web viewmar 04, 2021 · consider an internal combustion...

Documents