Energy Generation (DP IB Physics: SL)

• 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 = ½ × 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 = ½ × (ρvA) × v²

 P = ½ 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 before passing turbine: 1.15 kg m^-3
  • Blade length: 14 m
  • Air velocity after passing turbine: 4.5 m s^-1
  • Density after passing turbine: 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 × 10⁵ W

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

P = 0.5 × ρ × A × v³ = 0.5 × 1.30 × π × 14² × 4.5³ = 3.65 × 10⁴ W

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

P = (3.04 × 10⁵) - (3.65 × 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