Topic 8: Energy, power and climate change Can you read through the syllabus that Mr Porter is giving you?

Types of Energy Heat Chemical Light Gravitational Sound Elastic/strain Kinetic Nuclear Electric Stored/potential

The Law of Conservation of Energy Energy can be changed (transformed) from one type to another, but it can never be made or destroyed.

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 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 useful work.

Sankey Diagram The thickness of each arrow is drawn to scale to show the amount of energy

Efficiency Although the total energy out is the same, not all of it is useful.

Efficiency Efficiency is defined as Efficiency = useful energy output total energy input

Topic 8 – Lesson 2 Workings of a generator Energy sources Renewable and non-renewable Energy density

Electromagnetic induction If a magnet is moved inside a coil an electric current is induced (produced)

Electromagnetic induction A electric current is induced because the magnetic field around the coil is changing.

Generator/dynamo A generator works in this way by rotating a coil in a magnetic field (or rotating a magnet in a coil)

Non-renewable Finite (being depleted – will run out) In general from a form of potential energy released by human action Coal, oil, gas (fossil fuels), Uranium.

Renewable Mostly directly or indirectly linked with the sun The exception is tidal energy Photovoltaic cells, active solar devices, wind, wave, tidal, biomass.

World energy production Fuel % total energy production CO2 emission g.MJ-1 Oil 40 70 Natural gas 23 50 Coal 90 Nuclear 7 - Hydroelectric Others < 1

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 simply the heat of combustion

Energy density Coal - 30 MJ.kg-1 Wood - 16 MJ.kg-1 Gasoline – 47 MJ.kg-1 Uranium – 7 x 104 GJ.kg-1 (70000000 MJ.kg-1)

Hydroelectric energy density? Imagine 1 kg falling 100m. Energy loss = mgh = 1x10x100 = 103 J If all of this is turned into electrical energy it gives an “energy density” of the “fuel” of 103 J.kg-1

Electricity production Generally (except for solar cells) a turbine is turned, which turns a generator, which makes electricity.

Fossil fuels In electricity production they are burned, the heat is used to heat water to make steam, the moving steam turns a turbine etc.

Fossil fuels - Advantages Relatively cheap High energy density Variety of engines and devices use them directly and easily Extensive distribution network in place

Fossil fuels - Disadvantages Will run out Pollute the environment (during mining sulphur and heavy metal content can be washed by rain into the environment) Oil spillages etc. Contribute to the greenhouse effect by releasing greenhouse gases

Example question A coal powered power plant has a power output of 400 MW and operates with an overall efficiency of 35%

Calculate the rate at which thermal energy is provided by the coal A coal powered power plant has a power output of 400 MW and operates with an overall efficiency of 35% Calculate the rate at which thermal energy is provided by the coal

Calculate the rate at which thermal energy is provided by the coal A coal powered power plant has a power output of 400 MW and operates with an overall efficiency of 35% Calculate the rate at which thermal energy is provided by the coal Efficiency = useful power output/power input Power input = output/efficiency Power input = 400/0.35 = 1.1 x 103 MW

A coal powered power plant has a power output of 400 MW and operates with an overall efficiency of 35% Calculate the rate at which coal is burned (Coal energy density = 30 MJ.kg-1)

A coal powered power plant has a power output of 400 MW and operates with an overall efficiency of 35% Calculate the rate at which coal is burned (Coal energy density = 30 MJ.kg-1) 1 kg of coal burned per second would produce 30 MJ. The power station needs 1.1 x 103 MJ per second. So Mass burned per second = 1.1 x 103/30 = 37 kg.s-1 Mass per year = 37x60x60x24x365 = 1.2 x 109 kg.yr-1

A coal powered power plant has a power output of 400 MW and operates with an overall efficiency of 35% The thermal energy produced by the power plant is removed by water. The temperature of the water must not increase by more than 5 °C. Calculate the rate of flow of water.

Rate of heat loss = 1.1 x 103 – 0.400 x 103 = 740 MW A coal powered power plant has a power output of 400 MW and operates with an overall efficiency of 35% The thermal energy produced by the power plant is removed by water. The temperature of the water must not increase by moe than 5 °C. Calculate the rate of flow of water. Rate of heat loss = 1.1 x 103 – 0.400 x 103 = 740 MW In one second, Q = mcΔT 740 x 106 = m x 4200 x 5 m = 35 x 103 kg So flow needs to be 35 x 103 kg.s-1

Controlled fission (see topic 7) The chain reaction can be controlled using control rods and a moderator. The energy can then be used (normally to generate electricity).

Moderator This slows the free neutrons down, making them easier to absorb by the uranium 235 nuclei. Graphite or water is normally used. 1 eV neutrons are ideal)

Control rods These absorb excess neutrons,making sure that the reaction does not get out of control. Boron is normally used.

Heat The moderator gets hot from the energy it absorbs from the neutrons.

Heat This heat is used to heat water, to make steam, which turns a turbine, which turns a generator, which makes electricity.

Useful by-products Uranium 238 can also absorb neutrons to produce plutonium 239 which is itself is highly useful as a nuclear fuel. It makes more fuel!!!

Nuclear power - Advantages High power output Large reserves of nuclear fuels No greenhouse gases

Nuclear power - disadvantages Waste products dangerous and difficult to dispose of Major health hazard if there is an accident Problems associated with uranium mining Nuclear weapons

The solar constant The sun’s total power output is 3.9 x 1026 W! Only a fraction of this power actually reaches the earth, given by the formula I (Power per unit area) = P/4πr2 For the earth this is 1400 W.m-2 and is called the solar constant

The solar constant For the earth this is 1400 W.m-2 and is called the solar constant This varies according to the power output of the sun (± 1.5%), distance from sun (± 4%), and angle of earth’s surface (tilt)

Solar power - advantages “Free” Renewable Clean

Solar power - disadvantages Only works during the day Affected by cloudy weather Low power output Requires large areas Initial costs are high

Hydroelectric power

Water storage in lakes “High” water has GPE. AS it falls this urns to KE, turns a turbine etc.

Pumped storage Excess electricity can be used to pump water up into a reservoir. It acts like a giant battery.

Tidal water storage Tide trapped behind a tidal barrage. Water turns turbine etc.

Hydroelectric - Advantages “Free” Renewable Clean

Hydroelectric - disadvantages Very dependent on location Drastic changes to environment (flooding) Initial costs very high

Wind power Calculating power

Wind moving at speed v, cross sectional area of turbines = A

Wind moving at speed v, cross sectional area of turbines = A Volume of air going through per second = Av Mass of air per second = Density x volume Mass of air per second = ρAv A

Wind moving at speed v, cross sectional area of turbines = 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 = ½ρAv3 A

Wind power - advantages “Free” Renewable Clean Ideal for remote locations

Wind power - disadvantages Works only if there is wind! Low power output Unsightly (?) and noisy Best located far from cities High maintainance costs

Wave power

OWC Oscillating water column

Modeling waves We can simplfy the mathematics by modeling square waves. λ L 2A

Modeling waves If the shaded part is moved down, the sea becomes flat. λ L 2A

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

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

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

Modeling waves Loss of Ep per unit time = A2gLρ(λ/2) x v/λ = (1/2)A2Lρgv λ L 2A

Modeling waves The maximum power then available per unit length is then equal to = (1/2)A2ρgv λ L 2A

Power per unit length A water wave of amplitude A carries an amount of power per unit length of its wavefront equal to P/L = (ρgA2v)/2 where ρ is the density of water and v stands for the speed of energy transfer of the wave

Wave power - Advantages “Free” Reasonable energy density Renewable Clean

Wave power - disadvantages Only in areas with large waves Waves are irregular Low frequency waves with high frequency turbine motion Maintainance and installation costs high Transporting power Must withstand storms/hurricanes

Global Warming

The Sun The sun emits electromagnetic waves (gamma X-rays, ultra-violet, visible light, infra-red, microwaves and radio waves) in all directions.

The earth Some of these waves will reach the earth

Reflected Around 30% will be reflected by the earth’s atmosphere. This is called the earth’s albedo (0.30). (The moon’s albedo is 0.12) Albedo is the ratio of reflected light to incident light. 30%

Albedo The albedo depends on the ground covering (ice = high, ocean = low), cloud cover etc.

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

Absorbed by the earth This absorbed solar energy is re-radiated at longer wavelengths (in the infrared region of the spectrum) Infrared 70%

In order to understand some of these processes we need to know a little physics.

Black-body radiation Need to “learn” this!

Black-body radiation Black Body - any object that is a perfect emitter and a perfect absorber of radiation object does not have to appear "black" sun and earth's surface behave approximately as black bodies

Black-body radiation The amount of energy per second (power) radiated from a body depends on its surface area and absolute temperature according to P = eσAT4 where σ is the Stefan-Boltzmann constant (5.67 x 10-8 W.m-2.K-4) and e is the emissivity of the surface (=1 for a black object)

Wien’s law λmaxT = constant (2.9 x 10-3 mK)

Example By what factor does the power emitted by a body increase when its temperature is increased from 100ºC to 200ºC?

Example By what factor does the power emitted by a body increase when its temperature is increased from 100ºC to 200ºC? Emitted power is proportional to the fourth power of the Kelvin temperature, so will increase by a factor of 4734/3734 = 2.59

Surface heat capacitance Cs Surface heat capacitance is defined as the energy required to increase the temperature of 1 m2 of a surface by 1 K. Cs is measured in J.m-2.K-1. Q = ACsΔT

Example Radiation of intensity 340 W.m-2 is incident on the surace of a lake of surface heat capacitance Cs = 4.2 x 108 J.m-2.K-1. Calculate the time to increase the temperature by 2 K. Comment on your answer.

Example Each 1m2 of lake receives 340 J.s-1 Radiation of intensity 340 W.m-2 is incident on the surface of a lake of surface heat capacitance Cs = 4.2 x 108 J.m-2.K-1. Calculate the time to increase the temperature by 2 K. Comment on your answer. Each 1m2 of lake receives 340 J.s-1 Energy needed to raise 1m2 by 2 K = Q = ACsΔT = 1 x 4.2 x 108 x 2 = 8.4 x 108 J Time = Energy/power = 8.4 x 108/340 = 2500000 seconds = 29 days Sun only shines approx 12 hours a day so would take at least twice as long

Absorbed by the earth This absorbed solar energy is re-radiated at longer wavelengths (in the infrared region of the spectrum) Infrared 70%

Absorbed Various gases in the atmosphere can absorb radiation at this longer wavelength (resonance) H O They vibrate more (become hotter) O C H H C H H H O

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

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

Balance This means that normally the earth has a fairly constant average temperature (although there have been big changes over thousands of years) Energy in Energy out

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

Greenhouse gases Most scientists believe that we are producing more of the gases that absorb the infra-red radiation, thus upsetting the balance and producing a higher equilibrium earth temperature. This is called the enhanced greenhouse effect.

What might happen? Polar ice caps melt

What might happen? Higher sea levels and flooding of low lying areas as a result of non-sea ice melting and expansion of water

Coefficient of volume expansion Coefficient of volume expansion is defined as the fractional change in volume per unit temperature change

Coefficient of volume expansion Given a volume V0 at temperature θ0, the volume after temperature increase of Δθ will increase by ΔV given by ΔV = γV0Δθ

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.

Evaporation? Greater area cos of flooding? Uniform expansion? Example The area of the earth’s oceans is about 3.6 x 108 km2 and the average depth is 3.7 km. Using γ = 2 x 10-4 K-1, estimate the rise in sea level for a temperature increase of 2K. Comment on your answer. Volume of water = approx depth x area = 3.6 x 108 x 3.7 = 1.33 x 109 km3 = 1.33 x 1018 m3 ΔV = γV0Δθ ΔV = 2 x 10-4 x 1.33 x 1018 x 2 = 5.3 x 1014 m3 Δh = ΔV/A = 5.3 x 1014/3.6 x 1014 = 1.5 m Evaporation? Greater area cos of flooding? Uniform expansion?

What else might happen? More extreme weather (heatwaves, droughts, hurricanes, torrential rain)

What might happen? Long term climate change

Evidence? Ice core research Weather records Remote sensing by satellites Measurement!