IB DP Physics: SL复习笔记8.1.5 Energy Generation

Energy Generation

  • 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

8.4.6-Nuclear-Reactor-Components

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

7.3.3-Shielding

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

8-1-5-fossil-fuel-power-plant_sl-physics-rn

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

8-1-5-two-types-wind-turbine_sl-physics-rn

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

8-1-5-hydroelectric-power_sl-physics-rn

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

Calculating Energy Transformations

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

8-1-5-maximum-power-turbine_sl-physics-rn

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

Worked Example

Air moving at speed 9.5 m s-1 with a density of 1.15 kg m-3 is incident on a wind turbine. The length of the blades in the wind turbine are 14 m. After passing the wind turbine, the air is moving with a speed of 4.5 m s-1 and has a density of 1.30 kg m-3. Deduce the maximum power possible every second from this situation.

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:

8.1.5-Equation-1

  • 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

8.1.5-Equation-2

  • Substituting this into the power equation gives:

8.1.5-Equation-3

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

Worked Example

In a hydroelectric dam, water of density 1000 kg m−3flows with a flow rate: 75 × 10−3 m3 s−1goes through a turbine and descends approximately 22 m. Deduce the maximum power this will give if the efficiency of the turbine system is 85%.

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

8.1.5-Equation-4

    • 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

 

 

 

 

 

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