Energy sources

The limited resources of fossil fuel and their  impact of their use on global warming has led to the development of alternative sources of energy. 

• Primary energy is found in nature and has not been processed. 
• Non-renewable sources of energy are finite sources, which are depleted at a rate faster than they can be produced. They include fossil fuels (e.g. oil, natural gas and coal) and nuclear fuels (e.g. uranium).
• Fossil fuels have been produced over millions of years when buried animal and plant matter has been decomposed by bacteria under high pressure. Their energy ultimately originates from the Sun’s radiated energy which was originally captured by plants during photosynthesis millions of years ago.
• Renewable sources of energy include solar energy, wind energy, wave energy, bio-fuels and tidal energy. Wind energy, wave energy, bio-fuels, sustainable sources (e.g. wood when used sustainably) are indirectly dependent on solar energy.
• The specific energy $\rm (E_S)$ of a fuel is the amount of energy that can be obtained from a unit mass of the fuel. It is measured in $\rm J kg^{-1}$.
• The energy density $\rm (E_D)$ of a fuel is the amount of energy that can be obtained from a unit volume of the fuel. It is measured in $\rm J m^{-3}$.
  

• When primary energy is processed or exploited, secondary energy is produced.
• Secondary energy must be suitable for use in machines which perform mechanical work. Electricity is a very versatile form of secondary energy.
• The quantity of energy is always conserved, but not the quality as it becomes less useful, and cannot be used to perform mechanical work. This energy degradation occurs when thermal energy is transferred to the surroundings. It is degraded energy as it cannot be used to perform useful work.
• A heat engine converts heat to work. A cylinder of gas is heated, the gas expands and does work. The gas is then cooled and returns to its original volume ready for the process to be repeated. To operate, some heat must be transferred from a hot body to a cold one and thermal energy is lost to the surroundings.
• In a turbine, used in most power stations, heated water is converted to steam which causes the turbine blades to rotate.
• A generator consists of a rotating coil in a magnetic field or a rotating magnet in a coil. This induces an emf as the magnetic flux through the coil changes according to Faraday’s Law.

Worked Example

Show that $\rm E_{D}=\rho E_{S}$ where $\rho$ is the density of the fuel.

• Most primary energy sources are used to produce electricity.
• Efficiency of an energy transfer $= \dfrac{\text{useful output energy}}{\text{total input energy}} \times 100\%$

• In a fossil fuel power plant the fuel is burnt and the heat produced converts water into steam in the boilers. This pressurised steam forces a turbine to turn which makes the coils of a generator rotate in a magnetic field, creating electricity by electromagnetic induction. Cold water (usually from a nearby river) condenses the steam back into liquid water that can again be heated in the boilers. The greenhouse gas carbon dioxide is produced during the combustion of the coal.
• A Sankey diagram is an arrow block diagram which is used to represent energy flows. The width of the arrow is proportional to the amount of energy being transferred.

• Natural gas power plants have higher efficiencies $(\approx 50\%)$ than coal $(\approx 36\%)$ and produce less greenhouse gas emissions.
  

  Advantages of fossil fuels	Disadvantages of fossil fuels
  High specific energy Many engines are designed for their use Distribution network exists	Non-renewable Environmental problems due to leakages Produce greenhouse gases when burnt

• Uranium$-235$ is often used as the nuclear fuel as it undergoes nuclear fission reactions. For example:
  $\rm ^1_0 n + ^{235}_{92}U \rightarrow ^{236}_{92} U \rightarrow ^{144}_{56}Ba + ^{89}_{36} Kr + ^{31}_0 n$
• The neutrons produced in a fission reaction can collide with other uranium$-235$ nuclei and initiate more reactions.
  
• A chain reaction occurs when there is sufficient mass of uranium-235 present – the critical mass - to prevent the neutrons escaping without causing further reactions.
• The neutrons produced in the fission reactions must be slowed down by a moderator if they are to initiate other fission of other nuclei.
• Boron control rods absorb excess neutrons when it is necessary to control the rate of energy production.
  

  Advantages of nuclear fission energy	Disadvantages of nuclear fission energy
  High power output/specific energy Large reserves of nuclear fuels No greenhouse gases produced	Radioactive waste difficult to dispose of Potential major public health hazard if reactor becomes uncontrolled Could facilitate the production of nuclear weapons

• Nuclear fusion is a possible source of energy. For example, the reaction:
  $\rm ^2_1 H + ^2_1H \rightarrow ^3_2 He + ^1_0 n$
  This poses many challenging practical problems and is not yet commercially viable. Very high temperatures are needed, and the plasma formed (electrons disassociated from nuclei) must be confined.
• High temperatures and high pressures are needed as the reacting nuclei are positively charged and so repel each other.
  

  Advantages of nuclear fusion energy	Disadvantages of nuclear fusion energy
  High power output/specific energy The hydrogen in water can be used as the fuel Minimal radioactive waste products	Not commercially viable

• The Sun's total power output $\rm (P) = 3.9 \times 1~026~W$. The intensity of the radiation at the Earth's mean distance from the Sun $\rm (I) = P / 4 \pi d^{2} \approx 1~360~Wm ^{-2}$. This is the solar constant $\bf (S)$.
• The solar constant $\bf (S)$. is average value as the Earth follows an elliptical orbit around the Sun and the sun's output varies during a $11-$year cycle.
• The solar power incident per unit area at a particular point on the Earth's surface varies with the angle at which the solar rays hit the surface. The intensities decrease at smaller angles as the rays spread out.
• There are two different ways to extract energy from solar radiation.
  • Photovoltaic systems: solar to electric
    Sunlight incident on the cell, causes a separation of charge in a semiconductor and produces a small dc current and voltage. Many cells are needed in combination if higher voltages or currents are needed.
  • Solar active devices: solar to thermal
    Thermal energy from the sunlight is used to heat water for domestic use. These simple devices are inexpensive and are usually put on the roof of a house. They are bulky and need large spaces.
    

    Advantages of solar energy	Disadvantages of solar energy
    Sunlight is free and inexhaustible No pollution Photovoltaic cells are easy to maintain as no moving parts	Works only during the sunlight   Affected by cloudy weather Requires large areas High initial costs for photovoltaic cells

• The source of energy is the gravitational potential energy of water.
• The water can gain its gravitational potential energy in several ways.
  • Rain can fall on highlands
  • Tidal power schemes can trap water at high tides
  • Water can be pumped from a lower to higher levels. This pumped storage system provides a large-scale method for storing energy. Electrical energy can be used at a time of low demand to move the water uphill. This water is then released to generate electricity when the demand is high.
• The potential energy can be converted to kinetic energy as the water moves downhill which rotates turbines and generates electricity.

Consider a mass $\rm m$ of water that falls down a vertical height $\rm h$.
The potential energy is converted into kinetic energy when the mass falls the vertical distance $\rm h$.
$\rm E _{ P }=m g h$
Power $\rm P=$ rate of change of energy.
$\rm =m g h / \Delta t$
$\rm =\rho g h(\Delta V / \Delta t)$
$\rho$ is the density of water and $\rm \Delta V$ is the volume.

• The source of the wind’s kinetic energy is the sun. Different parts of the atmosphere are heated to different temperatures which result in pressure differences which cause air movements.
• Consider the amount of mass that passes through a cylinder of cross-sectional area $\rm A$ with velocity $v$. Let $\rho$ ; be the density of air.
  
  Mass of air $\rm (m)$ that passes through $\rm A$ in $1 \mathrm{sec} = \rho \mathrm A v$.
  The kinetic energy of air $=1 / 2 \mathrm m v^{2}$ $=1 / 2(\rho \mathrm A v) v^{2}$ $=1 / 2 \rho \mathrm A v^{3}$
  This is the power $\mathrm{(P) ~P}=1 / 2 \rho \mathrm A v^{3}$
  Assuming all the energy is given to the turbines: $\text{Wind power} \mathrm P=1 / 2 \rho \mathrm A v^{3}$