• You need to know about the main ways of generating electricity:
  • The equipment involved
  • The advantages and disadvantages
  • Calculate power obtained for different setups
• These revision notes cover:
  • Nuclear Power
  • Burning Fossil Fuels
  • Wind Electricity Generators
  • Hydroelectric Power
  • Solar Power

Nuclear Power

Control Rods & Moderators:

• In a nuclear reactor, a chain reaction is required to keep the reactor running
• When the reactor is producing energy at the correct rate, two factors must be controlled:
  • The number of free neutrons in the reactor
  • The energy of the free neutrons
• To do this, nuclear reactors contain?control rods?and?moderators

The overall purpose of a nuclear reactor is to collect the heat energy produced from nuclear reactions

Control Rods:

Purpose of a control rod:?To absorb neutrons

• Control rods are made of a material which absorb neutrons without becoming dangerously unstable themselves
• The number of neutrons absorbed is controlled by varying the depth of the control rods in the fuel rods
  • Lowering the rods further?decreases?the rate of fission, as more neutrons are absorbed
  • Raising the rods?increases?the rate of fission, as fewer neutrons are absorbed

• This is adjusted automatically so that exactly one fission neutron produced by each fission event goes on to cause another fission
• In the event the nuclear reactor needs to shut down, the control rods can be lowered all the way so no reaction can take place

Moderator:

The purpose of a moderator:?To slow down neutrons

• The moderator is a material that surrounds the fuel rods and control rods inside the reactor core
• The fast-moving neutrons produced by the fission reactions slow down by colliding with the molecules of the moderator, causing them to lose some momentum
• The neutrons are slowed down so that they are in?thermal equilibrium?with the moderator, hence the term ‘thermal neutron’
  • This ensures neutrons can react efficiently with the uranium fuel

Shielding:

• The entire nuclear reactor is surrounded by?shielding?materials
• The purpose of shielding is to?absorb hazardous radiation
• The daughter nuclei formed during fission, and the neutrons emitted, are radioactive
• The reactor is surrounded by a?steel?and?concrete?wall that can be nearly 2 metres thick
• This absorbs the emissions from the reactions
  • It ensures that the environment around the reactor is?safe

Shielding metals in a nuclear reactor

Advantages & Disadvantages of Nuclear Power

• Advantages?of using nuclear power include:
  • Extensive reserves of fissionable materials
  • Increasingly refine technology available
  • No greenhouse gases produced
  • A large amount of power is produced

• Disadvantages?of using nuclear power include:
  • Hazardous radioactive waste materials produced
  • Dangerous if the power plant goes significantly wrong
  • Danger of misuse of nuclear material
  • Problems with mining fuel

Burning Fossil Fuels

• Fossil fuels, such as coal and oil, are used to produce energy?on-demand?when energy is needed
  • This is done by?burning?the materials when the energy is required
• When fossil fuels are burned, it is used to?heat water
  • This water is heated until it becomes?steam
• Steam is forced around the system and this turns?a turbine
• The turbine spins and is connected to a?generator?which generates electricity
  • This electricity is carried out of the system by?electrical?lines
• The steam within the turbine will cool and?condense?and then be pumped back into the boiler to?repeat the process

Diagram of a Fossil fuel based Reactor. The overall purpose of the reactor is to collect the heat energy produced from burning fossil fuels

• The approximate?efficiency?of fossil-fuel based power plants is approximately?40%
  • Energy is?lost?to heat within exhaust gases, heat loss in the condenser process and friction within the system

Advantages & Disadvantages of Fossil Fuels

• Advantages?of using fossil fuel based power plants include:
  • Extensive infrastructure in place
  • High energy density of fuel
  • Available energy at any time
  • Well-known and developed technology

• Disadvantages?of using fossil fuel based power plants include:
  • Produces greenhouse gases
  • Unsustainable (non-renewable)
  • Produces pollution

Wind Electricity Generators

• Wind generators can be principally horizontally or vertically aligned
  • The majority of modern designs use?horizontally?aligned designs

The two main designs of wind generators: horizontal and vertical alignment

• The approximate?efficiency?of wind generators is approximately?30%
  • Energy is?lost?to aerodynamic limits, losses transferring the electricity to the grid and friction within the system

Advantages & Disadvantages of Wind Power

• Advantages?of using wind-powered generators include:
  • Clean (non-polluting) energy generation
  • Freely available
  • Is always sustainable and will never run out

• Disadvantages?of using wind-powered generators include:
  • Not consistent energy production
  • Needs favourable local conditions to be placed in windy locations
  • Can be visually unappealing

Hydroelectric Power

• Hydroelectric power using water stored at a height?h, that mass of water?m, is allowed to flow through turbines being pulled down by the acceleration due to gravity?g
  • The falling water has?stored gravitational potential energy?which is released when falling and used to?spin turbines?that?generate electricity

• Energy can be?stored for later?use?by pumping?water back up to a?higher?location to be released to a lower location and spinning the turbines again when needed
• The approximate?efficiency?of hydroelectric power generation is approximately?90%
  • Energy is?lost?to friction and other resistive forces

• The approximate?maximum power?that can be generated from a hydroelectric generator can be?estimated?by considering the rate of change of potential energy of the water falling through the turbines

A hydroelectric power generation station. In off-peak hours water can be pumped back to the higher reservoir.

Advantages & Disadvantages of Hydroelectric Power

• Advantages?of using hydroelectric generators include:
  • Clean (non-polluting) energy generation
  • Is sustainable
  • Can be stored for when needed

• Disadvantages?of using hydroelectric generators include:
  • Large areas and changes to the environment are needed
  • It relies on suitable locations
  • A large initial investment is required

Wind Electricity Generators

• The approximate?maximum power?obtained per second that can be generated from a horizontal wind generator can be?estimated?by considering the blade radius and an incoming column of air

A column of air can provide only a limited amount of energy for a wind generator of blade radius r

• A column of air of density?ρ?can move through a cross-sectional area?A?which is determined by the blade radius?r
  • The amount of air that can move through this region is dependent on the velocity of the air?v?and the time considered?t
• The kinetic energy of the air arriving at the turbine every second can be described by:

KE?=???×?mass?×?velocity²

• The?mass,?m, of the column of air can be described by using the equation

m?=?ρV?=?ρAL

• Where:
  • ρ = density of the air (kg m^?3)
  • V?= volume of the column (m³)
  • A?= cross-sectional area of the column (m²)
  • L?= length of the column (m)

• The length of the column can be described by

L?=?vt

• Where:
  • v = velocity of the air (m s^?1)
  • t = time taken to travel the length of the column (s)

• Since the case is being considered for every second, time,?t?= 1 s
• Therefore, mass, in this case, will be:

m = ρvtA?=?ρvA

• This means power obtained per second can be described by:

P?=???×?(ρvA)?×?v²

P?=???ρAv³

• This equation shows that the main variable that can impact power generated by wind is the wind's velocity
  • If the wind's velocity remains the same, but the area covered by the blades doubles, then the theoretical power will double
  • Yet, if the area covered by the blades remains the same and the wind velocity doubles, then the theoretical power available will increase eight-fold
• Typical values of quantities are useful to be aware of:
  • Density of the air = 1.3 kgm^?3?at standard temperature and pressure
  • Velocity of the air required to turn the blades = 12 kmh^?1?to get them turning and then 70 kmh^?1?at full capacity
  • Radius of the wind turbine blade = 50 - 150 m

Step 1: List known values

• • Air velocity before passing turbine: 9.5 m s^-1
  • Air density: 1.15 kg m^-3
  • Blade length: 14 m
  • Air velocity after passing turbine: 4.5 m s^-1
  • Density: 1.30 kg m^-3

Step 2: Find maximum power available

P = 0.5?×?ρ × A ×?v³?= 0.5 × 1.15 × π × 142?× 9.5³?= 3.04 × 10⁵W

Step 3: Find the remaining power within the air after passing the turbine

P = 0.5?×?ρ × A ×?v³= 0.5 × 1.15 × π × 142?× 4.5³= 3.64 × 10⁴?W

Step 4: Find the power available for the turbine to use

P = (3.04 × 10⁵) -?(3.64 × 10⁴) = 2.68?× 10⁵?W

Step 5: State the final answer

• • The?maximum power?available to the turbine is:?2.68?× 10⁵?W?every second

Hydroelectric Power

• Consider water of mass m stored at a height?h, that is allowed to flow through turbines being pulled down by the acceleration due to gravity?g
  • The gravitational potential energy of the water is?m × g × h
• Therefore, the change in energy (the power) will be:

• Where Δt =?the time taken for the change in energy to occur

• This can be re-written in terms of volume and density rather than mass to consider the equation in terms of the?volume flow rate

• Substituting this into the power equation gives:

• Therefore, to get large energy from hydroelectric power, large flow rates?(ΔV ÷ Δt)?and heights?h?are needed to maximise the energy produced

Step 1: List the known quantities

• • Flow rate,?ΔV /?Δt?= 75?× 10^?3?m3?s^?1
  • Height of water drop,?h?= 22 m
  • Density of water,?ρ = 1000 kg m^?3
  • Efficiency of turbine system, e = 85%

Step 2: State the relevant equation for hydroelectric power

• • P?= power (W)
  • ρ = density (kg m^-3)
  • g?= acceleration due to gravity (m s^?2)
  • h?= height of falling water (m)
  • ΔV /?Δt?= the flow rate (m³?s^?1)
  • e?= efficiency [no units]

Step 3: Substitute in the values

P?= (1000 × 9.8 × 22) × (75 × 10^?3) × 0.85 = 1.37 x 10⁴?W

Step 4: State final answer

• • The approximate power available for the situation is:?1.37 × 10⁴?W