Energy, work and power

Key points

1.7.1 Energy

• Energy is measured in joules (J).
• Energy can be held in different stores:
  • kinetic: the energy of a moving object
  • gravitational potential: the energy of an object because of its height in a gravitational field
  • chemical: energy in fuels, food and batteries, released by chemical reactions
  • elastic (strain): energy in an object that is stretched, squashed or bent, such as a spring
  • nuclear: energy in the nuclei of atoms, released in nuclear reactions (see 5.1)
  • electrostatic: energy of electric charges that attract or repel each other
  • internal (thermal): energy of the particles of an object; it increases when the object gets hotter
• Energy is transferred from one store to another in four ways:
  • by forces: mechanical work done
  • by electric currents: electrical work done
  • by heating
  • by waves: electromagnetic waves, sound and other waves
• Examples of energy transfers:
  • Throwing a ball upwards: the ball’s kinetic store goes down and its gravitational potential store goes up. The transfer is by a force: the ball’s weight acts against its motion as it rises.
  • Electric kettle: an electric current does electrical work on the heating element. The element heats the water. The internal (thermal) store of the water increases.
  • Ferry engine: the chemical store of the diesel goes down. Forces transfer energy to the kinetic store of the ferry. Some energy goes to the internal (thermal) store of the engine and the surroundings by heating. Some is carried away by sound waves.
  • Solar cell: light (an electromagnetic wave) from the Sun transfers energy to the cell. The cell makes a current, which does electrical work, for example charging a battery (chemical store).
• Conservation of energy: energy cannot be created or destroyed. It can only be transferred from one store to another. The total amount of energy stays the same.
• So for any device: total energy input = useful energy output + wasted energy output.
• Wasted energy usually ends up in the internal (thermal) store of the surroundings. It is spread out, so it is hard to use again.
• A flow diagram shows the stores as boxes and the transfers as arrows. Light is a way of transferring energy, so it goes on an arrow, not in a box.
• Example for a torch: chemical store of the battery → (electrical work) → lamp → (light and heating) → internal (thermal) store of the surroundings. The surroundings absorb the light, and this warms them.
• Kinetic energy: E_k = ½mv². Extended
• Kinetic energy depends on v². If the speed doubles, the kinetic energy becomes four times as large. Extended
• Change in gravitational potential energy: ΔE_p = mgΔh, where Δh is the change in height. Extended
• Multi-stage transfers: apply conservation of energy at each stage. Example, a hydroelectric power station: gravitational potential store of the water behind the dam → kinetic store of the falling water → kinetic store of the turbine → electrical work done by the generator. Some energy is wasted at each stage. Extended
• Object released from rest: if air resistance is small enough to ignore, all the gravitational potential energy it loses becomes kinetic energy: mgΔh = ½mv². Extended
• With air resistance, some energy is transferred to the internal (thermal) store of the object and the air. So the object gains less kinetic energy than the gravitational potential energy it loses. Extended
• A Sankey diagram shows energy transfers as arrows. The width of each arrow is proportional to the amount of energy (or power). Extended
• In a Sankey diagram, the input arrow splits. The useful output goes straight on. The wasted output bends away. Extended
• The widths of the output arrows add up to the width of the input arrow. This shows conservation of energy. Extended
• Example: an electric motor takes in 100 J. It gives out 70 J of useful kinetic energy, 25 J to the internal (thermal) store of the surroundings and 5 J as sound. Check: 70 + 25 + 5 = 100 J. Extended

1.7.2 Work

• Work done is equal to the energy transferred. This is true for mechanical work done (by a force) and for electrical work done (by a current).
• Mechanical work: W = Fd = ΔE.
• d is the distance moved in the direction of the force.
• Work done is measured in joules (J). One joule of work is done when a force of 1 N moves an object 1 m in the direction of the force.
• If the object does not move, the force does no work. Example: holding a heavy bag still does no work on the bag.
• When you push a box across a rough floor at constant speed, the work done against friction is transferred to the internal (thermal) store of the box and the floor.

1.7.3 Energy resources

• Many power stations generate electricity in the same way:
  1. A boiler: an energy source heats water and turns it into high-pressure steam.
  2. A turbine: the steam pushes on the turbine blades and makes the turbine spin.
  3. A generator: the turbine turns the generator, which generates electricity (see 4.5).
• (a) Fossil fuels (coal, oil, natural gas): the fuel is burned to release the energy in its chemical store. The burning fuel heats water in a boiler and turns it into steam. The steam drives a turbine, which turns a generator.
• In a diesel generator, the fuel burns inside an engine. The engine turns the generator directly. There is no boiler and no steam turbine. Much of the electricity on Maldivian islands is generated in this way.
• (b) Biofuels (for example wood, plant oils and alcohol made from crops): the chemical store is released by burning. They are used like fossil fuels, to heat a boiler or to run an engine.
• (c) Water:
  • Waves: the up-and-down motion of the waves moves parts of a floating machine. This motion drives a generator.
  • Tides: a barrage (a dam) is built across a river mouth. As the tide rises and falls, water flows through turbines in the barrage. The turbines turn generators.
  • Hydroelectric dams: water is stored high up behind a dam. It has a gravitational potential store. The water flows down through turbines, which turn generators.
• (d) Geothermal: rocks deep underground are hot. Cold water is pumped down to them. It comes back up as steam or hot water, which drives a turbine and generator. The hot water can also heat buildings.
• (e) Nuclear fuel: in a nuclear reactor, uranium nuclei split (fission, see 5.1). This releases energy, which heats water in a boiler. The steam drives a turbine, which turns a generator.
• (f) Solar cells: light from the Sun falls on a solar cell. The cell turns the energy of the light directly into electrical energy. There is no turbine and no generator.
• (g) Solar panels: infrared and other electromagnetic waves from the Sun heat water that flows through pipes in the panel. This gives hot water for a building. A solar panel does not generate electricity.
• (g) Wind: the Sun heats the land and the sea by different amounts. Warm air rises and cooler air moves in to take its place. This moving air is wind. A sea breeze forms in this way. In a wind turbine, the wind turns the blades, and the blades turn a generator.
• Words used to compare energy resources:
  • Renewable: the resource is replaced by nature as fast as we use it, so it will not run out. A non-renewable resource will run out.
  • Availability: whether the resource can be used in a particular place.
  • Reliability: whether it can supply energy whenever it is needed.
  • Scale: how much electrical power it can supply.
  • Environmental impact: the harm it does, for example pollution, carbon dioxide (CO₂) emissions and damage to habitats.

• Efficiency tells you how much of the energy put into a device ends up as useful output.
• A more efficient device wastes less energy. Wasted energy is usually transferred to the internal (thermal) store of the surroundings.
• Most of the energy resources above get their energy, in the end, from the Sun’s radiation. The three exceptions are geothermal energy, nuclear fuel and tidal energy. Extended
• Why the Sun is the source: Extended
  • Fossil fuels formed from plants and animals that lived long ago. The plants got their energy from sunlight.
  • Biofuels come from plants, which grow using sunlight.
  • Wind is caused by the Sun heating the Earth’s surface unevenly. Waves are made by the wind.
  • For hydroelectric power, the Sun evaporates water. It falls as rain on high ground and fills the reservoir behind the dam.
• Why the three exceptions are different: geothermal energy comes from inside the Earth; nuclear fuel comes from rocks in the Earth; tides are caused mainly by the gravitational pull of the Moon. Extended
• The Sun releases energy by nuclear fusion: hydrogen nuclei join to make helium nuclei (see 6.2). Extended
• Research is being carried out into using nuclear fusion to generate electrical energy on a large scale. Extended
• Extra detail: this is difficult because fusion needs extremely high temperatures, and the very hot fuel must be held away from the walls of the reactor.
• Efficiency is defined as useful energy output ÷ total energy input. It can also be found from useful power output ÷ total power input. Multiply by 100% to give a percentage. Extended
• Efficiency has no unit. It can never be more than 1 (100%). It is less than 1 when some energy is wasted. Extended

1.7.4 Power

• Power is the work done per unit time: P = W / t.
• Power is also the energy transferred per unit time: P = ΔE / t.
• So power is the rate at which energy is transferred.
• The unit of power is the watt (W). One watt is one joule per second (1 W = 1 J/s).
• 1 kW = 1000 W. 1 MW = 1 000 000 W.
• A more powerful machine transfers the same energy in less time, or more energy in the same time.

Common mistakes

• Students write that energy is “lost” or “used up”. / The mark scheme wants: energy is transferred, often to the internal (thermal) store of the surroundings; the total stays the same.
• Students call the energy in a hot object “heat”. / The mark scheme wants the name of the store, internal (thermal) energy, and the name of the transfer, heating.
• Students write that a solar cell uses a turbine and generator, or that a solar panel makes electricity. / The mark scheme wants: a solar cell turns light directly into electrical energy; a solar panel heats water.
• Students write that “renewable” means “does not pollute”. / The mark scheme wants: a renewable resource is replaced naturally and will not run out.
• Students forget to square the speed in E_k = ½mv², or use a mass in grams. / The mark scheme wants v squared and the mass in kg. Extended
• Students give an efficiency above 100%, or divide the input by the output. / The mark scheme wants useful output ÷ total input. This can never be more than 1 (100%), and it is less than 1 when some energy is wasted. Extended
• Students write that tidal energy comes from the Sun. / The mark scheme wants: the Sun’s radiation supplies the energy for most resources, but not for geothermal, nuclear or tidal. Extended

Exam tips

• State the energy stores and the four ways energy is transferred. Use these exact names.
• Describe a transfer as “from store → by which transfer → to store”, for example “chemical store → by heating → internal (thermal) store of the water”.
• Describe how electricity is generated: name the boiler, turbine and generator in order, and say what each does. A solar cell has none of them. A wind turbine has no boiler: the wind turns the turbine, and the turbine turns the generator.
• When you compare resources, use the five words: renewability, availability, reliability, scale, environmental impact. Give one advantage and one disadvantage for each resource.
• Calculate power: check the time is in seconds. Convert kJ to J before dividing if the answer must be in W.
• Interpret a Sankey diagram: the outputs add up to the input; read the useful arrow and divide by the input to find efficiency. Extended
• Calculate in a multi-stage problem: write the energy at each stage and use conservation of energy to link them. State any assumption, for example “air resistance is ignored”. Extended
• A typical 1-mark answer: “Power is the energy transferred per unit time.”
• A typical 2-mark answer to “Describe how a hydroelectric station generates electricity”: “Water stored behind the dam flows down through turbines (1). The turbines turn generators (1).”
• A typical answer to “Name the three energy resources that do not get their energy mainly from the Sun”: “Geothermal, nuclear and tidal.” Extended
• A typical 3-mark answer to “Give one advantage and two disadvantages of solar cells in the Maldives”: “There is a lot of sunshine and no fuel is needed (1). They give no output at night (1). They need a large area, and land on the islands is limited (1).”