Some ways of talking about energy are clearer and more helpful than others.

Energy stores

It is helpful to talk about energy stores. A spring, or a rubber band, can rather obviously store energy. You do work to stretch them (or to squash the spring), and you can get back pretty much the same amount of energy when they relax. These then are two of the best iconic examples for grasping what ‘potential energy’ is all about. It is energy in a mechanical store.

Many students find the term ‘potential’ confusing. They think ‘potential energy’ is somehow different from actual energy. Talking about energy stores offers a way of deferring the term ‘potential energy’ until later, for students who choose to continue studying physics.

You can similarly feel energy being stored when magnets are pushed together or pulled apart.

The example nearly all textbooks give of potential energy is perhaps the most difficult of all. It is the gravitational energy of a lifted mass. Now the energy is said to be ‘in’ the lifted object – as for a spring it is said to be ‘in’ the spring. If you have the courage, you could say that the energy is stored between the Earth and the lifted object (in the gravitational field). The trouble is of course that an external examiner might score that truthful answer as wrong because specialist understanding is not required at this level.

Another kind of energy store is a mixture of fuel and oxygen. In this case bonds between carbon and oxygen atoms can snap shut, releasing energy in a fire or explosion. It is common to talk about just the fuel – for example petrol – as the energy store, but do remember that for this chemical spring to snap shut, there must be oxygen too.

There are a limited number of energy stores:

• chemical (e.g. fuel + oxygen)
• kinetic (in a moving object)
• gravitational (due to the position of an object in a gravitational field)
• elastic (e.g. in a stretched or compressed spring)
• thermal (in a warm object)
• magnetic (in two separated magnets that are attracting, or repelling)
• electrostatic (in two separated electric charges that are attracting, or repelling)
• nuclear (released through radioactive decay, fission or fusion)

Energy carriers (or pathways) and energy transfers

It is often helpful to think of energy being carried from one place to another. For example, light carries energy from the Sun to the Earth. Light is not itself ‘energy’ – it is after all an electromagnetic wave, or a stream of photons (however you care to look at it). But energy does travel with the light. The same is true of radio waves. In a microwave oven microwaves carry energy from the microwave generator to the interior of the food. Other kinds of waves carry energy too, for example ocean waves.

Electric current in a circuit is another energy carrier. It is helpful to think about a power circuit as a way of moving energy from one place to another. The National Grid distributes energy from a number of power stations, via the wires and cables, to homes and factories.

It is often handy to think of moving matter as carrying energy, too. A strong wind delivers energy to a wind turbine. But, equally often, it is better to think of the moving mass as storing energy. A train has to be given energy to get it moving, and energy has to be taken from the train to stop it. This is what we call kinetic energy.

Energy carriers (or pathways, or transfers)

• mechanically (when a force moves through a distance)
• electrically (when a charge moves through a potential difference)
• by heating (because of a temperature difference)
• by radiation (e.g. light, microwaves)

With all of these, we are interested in the rate at which energy is being transferred and not the amount stored anywhere.

You can use flow diagram representations to strengthen the distinction between energy stores and carriers, for example:

There are some very important scientific ideas in this way of looking at things. Among them are:

• that energy tends, in most cases, to spread from a more concentrated store to more dispersed stores; and that this makes it less useful for doing anything more
• that the energy often ends up warming the environment

Visit School Science Review for two useful papers: Richard Boohan Making sense of energy and Robin Millar 'Teaching about energy: from everyday to scientific understandings':

School Science Review

Many textbooks and teaching schemes talk of ‘transforming’ energy, or of ‘converting energy from one form to another’.

This is a very common way of talking, but it has its problems. Particularly, it is in danger of saying nothing at all. For example, “A torch converts chemical energy in the battery to light energy”. All this says is that a chemical reaction happens and light comes out.

It is easy to teach and learn the language of ‘transforming’ energy. Students can translate throwing a ball into ‘muscle energy is changed into kinetic energy’. But it is dangerously close to being no more than a game of words.

Describing chains of energy transfers, for example with a steam engine or electric motor lifting a load, particularly tends towards this kind of talk. Yet the energy in the motion of the moving parts is irrelevant to an understanding of the overall process. If, for example, a drive belt was replaced with a lighter one that otherwise had the same mechanical properties, it would have less energy – but the process would continue as before. The energy of the moving parts is not a useful quantity to know.

It is more useful to focus on the initial and final energy stores. This puts the emphasis on where the energy is and why, not on renaming it once it goes from one thing to another.

In some situations, the ‘forms of energy’ approach can easily lead to incorrect analyses of processes. For example, many textbooks discuss energy transfers in a car moving along a level road. It is common to show stored energy of the petrol being transferred to the car (kinetic energy) and heating parts of the car and the surroundings. This is correct for the period when the car is speeding up. But once the car is going at a steady speed (and so has constant kinetic energy), all of the stored energy is ultimately heating parts of the car and the surroundings, in part by pushing air out of the way.

The really important thing is to work from very early on with actual quantities of energy, to do plenty of simple sums about amounts of energy and rates of delivery. This is where there is real payoff; where something is actually being said, and understanding has something to get a grip on.

Including simple sums about energy and power is very important. It introduces the units that are in practical use, without much formality. It introduces both energy and power (rate of energy supply or use; a bit of trouble taken early over amount and rate of change will be repaid later).

• Nearly all foods are now labelled with their ‘energy content’ (how much energy is liberated when they are digested). Valuable energy lessons can be taught based on diet energy calculations.

An active grown man needs around 2,000 kilocalories per day (about 8400 kJ per day). Women generally need a bit less. The energy has to come from ‘burning’ food in the body. Most of this energy is ‘wasted’ through cooling (humans run at about 100 W). Only a relatively small fraction is expended in physical activity. (Note the dietary Calorie is a kilocalorie.)

• Heating water makes a useful start on measuring amounts of energy. An electric kettle is marked with the rate at which it delivers energy – its power. This is in watts, and is often about 2 kW. Multiply by the number of seconds it is switched on for, and you have the number of joules delivered. [Avoid calculating energy exchanges from electrical equations at an early stage.]

Heating a kettle of water to boiling point takes about 0.5 MJ, for example. Leaving a 100 W lamp on for 3 hours uses a bit more than 1 MJ. It’s worth comparing this with the amount of energy provided by a single meal.

• Collect from the class examples of household fuel bills: gas, electricity, oil. They can show how much energy is transferred to the home, and give pointers to where savings might be made.

The fuel bill for gas tells you how many cubic metres of gas you have burned. The bill for oil tells you how many litres of heating oil have been put in your tank. The electricity bill tells you how many kilowatt hours you have used. But all of them also convert these amounts to a common unit: say megajoules. [Note that 1 kW hour is 3.6 MJ]

The fact that all fuel uses can be expressed in a common unit reflects the deeper fact that fuel sources are interchangeable as far as energy is concerned. Heating a bath full of water by burning oil or by using electricity uses the same amount of energy for the water, even though the two methods may waste different amounts by letting energy leak elsewhere.

The teaching trick is to use the units for electricity supplies to give the units for energy and power:

Power = rate of supply of energy

1 watt = 1 joule per second

1 kW = 1000 J per second (1 kJ per second)

1 MW = 1 MJ per second = 1000 kJ per second

This calls for some work with the labels on a variety of electrical appliances. Each has its power on the label (even your computer). One can compare kettles, electric irons, refrigerators, washing machines, ovens, hair driers etc.

• Use Sankey diagrams to represent processes in energy terms.

This representation is useful in conveying the idea that the total amount of energy is the same at the beginning and end of a process, without having to state this explicitly.

Working out money costs is important in both making it seem real, and in keeping the ideas relevant. A good aim is to send students home with information their families will find interesting or surprising.

Most important, activities such as these make it clear that energy changes are the kind of thing you have to calculate , not just look at or chat about. At the same time, doing sums like this gives students a feeling of definiteness and practical use of the ideas. That will probably work better than logical definitions to make them feel secure.

In physics, there is a standard way to work out how much energy has been transferred. It is to calculate the work done.

Work is done when an applied force causes something to move in the direction of the force.

ΔE = work done = force x distance moved in the direction of the force.

Notice that no energy is shifted in the two situations below:

• when an object rests on a shelf – although the object has weight, there is no movement.
• if the force is perpendicular to the direction of movement - e.g. a satellite in orbit around the Earth.

This equation leads to the definition of the SI unit for energy, the joule: 1 joule is the work done when a 1 N force moves through a distance of 1 m.

For example, a motor or a human arm might raise kilogram masses onto different height shelves. The change in energy stored gravitationally can be calculated using the formula,

ΔE = weight x Δh =mgΔh, where Δh is the vertical distance a mass m has been raised, and g is the gravitational field strength.

Energy and the human body

However, there is more than this to working out how much energy has been transferred. When you lift bricks your body also gets warmer, due to the energy from digested food. It does not look as if there is any “force x distance” here. But the energy that is transferred by heating to make it warmer can be calculated in this way, and can be measured in the same unit, joules. (See food packets, labelling portions in kJ.)

Human beings are only about 25% efficient for doing mechanical jobs. For every 1,000 joules of energy which are transferred from fuel stored in muscles, only 250 joules are transferred to raising a load or doing some other kind of job. 750 joules are stored thermally (the body warms up). Thermodynamics shows that muscles could be more than 70% efficient in transferring their energy to do useful jobs, but only if the action was conducted infinitely slowly. So when estimating the useful energy transferred from energy stored in food to muscles in order to climb the stairs, for an eight hour day, then the answer needs to be multiplied by four to find the demand on food.

When a 1kg mass is raised by a height of 1 metre, then 10 J of energy is now stored gravitationally . This can be obtained from four grains of sugar, a mini-snack. One grain of sugar is for doing work to raise the load, and three grains are for heating the room. If you raise 1 kg through a height of 1 m every second requiring 1 mini-snack per second then this is about 10 grams of sugar per hour. Not enough to allow you to eat a cream-cake or a bar of chocolate without putting on weight (i.e. mass)!

Transferring energy electrically

Energy transferred electrically is calculated using the equation ΔE = IVt , where I is the current, V is the potential difference and t is time.

Heating with friction

In frictional rubbing, a force moves over a surface, but just makes it hot. You measure the rise in temperature of the material, and how much of it is warmed up. Then, next time something gets warmer, you know what amount of “force x distance” or work would have been needed if the warming up had been done in this way.

Sooner or later you’ll need to tell a story about what “getting hotter” means, in energy terms. It just means that the invisible atoms or molecules are moving about faster. Energy is stored kinetically by a large number of molecules. And it isn’t easy to claim it back again, because they have shared it out randomly amongst a huge number of particles.

There are plenty of practical examples of friction making something hotter. Car (or bicycle) brakes are a case where we want to transfer the energy of a moving car stored kinetically as speedily as possible. Exercise bicycles let students feel how what seems a large amount of mechanical work done produces only what seems like a modest heating effect.

A key teaching point is not to let ‘friction’ become a kind of excuse for things not working properly. It’s the way that the work done by forces ‘gets inside’ matter.

One of the problems about teaching energy effectively is that there has often been an emphasis on learning about ‘accepted’ qualitative descriptions; the key idea that energy is a quantitative concept used to solve real problems tends to get lost. Many people have emphasized the importance of introducing younger students to the idea that energy is quantitative, for example, by comparing the energy values given on food labels. Using secondary data like this is very helpful, but is not a substitute for students getting hands-on experience of obtaining their own data through practical measurements.

The SEP Energymeter was developed to enable students to get direct experience of measuring energy and power in low-voltage circuits (it can be used in circuits up to 10 V). The intention was to produce a low-cost instrument that schools could afford to buy in sufficient numbers to maximize the opportunities for hands-on activity, and to complement the existing meters for the domestic market that measure energy consumption for mains appliances.

Concepts such as temperature and force are no less difficult and subtle than energy, but they have acquired an apparent straightforwardness because it is possible to measure them directly. Similarly, for energy, if students can make their own measurements it can deepen their understanding of the concept.

SEP Energymeter

The energymeter has two sets of terminals – ‘source’ (1) and ‘load’ (2). In the example below, the diagram shows how the energymeter can be connected to make measurements on a domestic torch. Two batteries are connected to the ‘source’ terminals and the ‘load’ terminals are connected to the torch (by taking the cover off, removing the batteries and clipping the leads onto the contacts inside).

The energymeter is supplied with a 12 V DC mains adaptor which is plugged into a socket (5). When it is inserted, values will appear on the display panel (3).

The function knob (4) has four positions and allows the following measurements to be made:

• Energy
• Power
• Average power
• Voltage, current and power

The display of the energymeter automatically adjusts to use appropriate units for the values involved (for example, mJ, J or kJ), and automatically shifts the decimal point so that the display always shows values to three significant figures.

To measure the energy transferred from the batteries to the torch, the function knob is set to ‘Energy’ and the ‘start/pause’ button (6) is pressed. The display shows the total amount of the energy transferred, and the time elapsed since the button was pressed. Pressing the button again pauses the collection of data; pressing the reset button (7) sets the values back to zero.

With the function knob on the ‘Power’ setting, the display shows the value of the power at a particular moment in time (it refreshes every half-second).

The ‘Average power’ setting can be useful when there is a lot of variation in the power, such as using a hand-turned generator, a wind turbine, or a solar panel in varying light conditions.

To measure the voltage across the source and the current in the circuit, the function knob is turned to the ‘V, I and P’ setting. As well as voltage and current, the display shows the power (calculated from voltage x current).

The energymeter, in fact, works by measuring the voltage across the source and the current in the circuit, and calculating the power from these. From the power, it can then calculate the energy transferred over a period of time. The diagram below represents how the energymeter can be thought of as a combined voltmeter and ammeter.

Though the energymeter starts from measurements of voltage and power, conceptually, the sequence is reversed. Younger students can begin by using the energymeter to measure amounts of energy. They can then go on to measure power, developing an understanding that power is the rate of transfer of energy. Finally, older students can make measurements of voltage and current and relate these to power and energy.

There is a very wide range of experiments in which students get hands-on experience of measuring energy and power. The SEP publications ‘Making Energy Real: Using the SEP Energymeter’ and ‘Energy Storage’ give examples and suggestions for these.

These materials have been adapted from the booklet ‘Making Energy Real: Using the SEP Energymeter’ published by the Gatsby Science Enhancement Programme.

Energy is conserved. What does this really mean, and why is it true?

Water in a reservoir is more or less conserved. So the amount of water can always be calculated from the amount that was there some time ago, plus the amount that has come in, minus the amount that has gone out (you may have to take account of evaporation as well as water drawn off).

Another way of saying the same thing is that water can’t be made or destroyed. For there to be more, it has to come in; for there to be less it has to go out.

Energy is similar. If you take any volume of space, then the total energy inside that volume at a given time is always the amount that was there earlier, plus the total amount that has come in through the surface, minus the total amount that has gone out through the surface.

Another way of saying the same thing is that energy can’t be made or destroyed. For there to be more, it must have come from somewhere; for there to be less it must have gone somewhere else. This also means that energy is a calculable quantity. The practical teaching implication here is that it is important to do sums about energy changes – how much in, how much out – and not just to talk generally about it.

The conservation laws, such as the conservation of energy, give physics its backbone. They are not really statements of knowledge but they contain implicit assumptions and definitions. They are however tied to the natural world, and they contain experimental knowledge.

The emergence of energy physics

By the early 19th century, steam engines were widely used. Both physicist and engineers sought to understand them by developing a ‘theory of steam engines’. Through the 1840s, as part of this process, several key people developed the concept of energy and its conservation : Mayer, Joule, Helmholtz and Thomson.

Julius Mayer, a German physicist, was the first person to state the law of the conservation of energy, in an 1842 scientific paper. Mayer experimentally determined the mechanical equivalent of heat from the heat evolved in the compression of a gas (without appreciating that heat could be explained in terms of kinetic theory).

In 1847 another German physicist, Hermann von Helmholtz, formulated the same principle in a book titled On the Conservation of Force. By contrast with Mayer, Helmholtz did view heat as matter in motion. The idea of conservation arose from his interest in animal (body) heat. He may not have known about Mayer’s prior work.

Between 1839 and 1850 the English brewer James Joule conducted a remarkable series of experiments, seeking to unify electrical, chemical and thermal phenomena by demonstrating their inter-convertibility and their quantitative equivalence. His numerical results and conclusion were published in the Philosophical Transactions of the Royal Society with the title On the mechanical equivalent of heat.

William Thomson (later Lord Kelvin) took the next step, considering the problem of irreversible thermal processes, until that time simply a contradiction between Carnot and Joule. Carnot, in his 1824 theory of heat engines, had argued that heat could be lost; more recently Joule argued that energy was convertible from one form to another but could be destroyed. In Thomson’s 1851 scientific paper The Dynamical Equivalent of Heat, he contended that energy was "lost to man irrecoverably; but not lost in the material world". Thomson was thus the first person to understand that all energy changes involve energy dissipation.

From energy to thermodynamics

In the second half of the 19th century Thomson and other scientists (including Clausius, Rankine, Maxwell and, later, Boltzmann) continued to develop these ideas. Kinetic theory and the science of thermodynamics gradually became established, with energy conservation as its First law and energy dissipation as its Second law.

Physicists aim to understand, and sometimes to predict, physical interactions. They use two abstract concepts a lot: force and energy.

Force

A force is something that can change an object's shape or how it is moving (or not moving). A force can have any size and acts in a particular direction. Forces are something to think about when analyzing things such as:

• pressure
• turning effect
• momentum
• acceleration

The concept of force is used to explain what causes things to happen. You can analyze the forces acting on macroscopic objects or systems, but also on microscopic objects such as the particles in a gas. When forces acting on an object are in equilibrium (balanced), the velocity of the object does not change. If the object is at rest, it stays there. If the object is moving it doesn’t speed up, slow down or change direction.

Energy

Energy is a numerical value that we calculate for an object, or a system, that quantifies the amount of change that has taken, or will take, place. What is important about this quantity is that, in every event or process, there is the same amount of it at the end as there was at the beginning. Energy does not explain why things happen, though we can use it to explain why some things do NOT happen.

The concept of energy has much wider use than the concept of force. The concept of energy can provide insights into movement and materials. It can also be used to analyze electrical and magnetic behaviour, wave behaviour, changes inside the atom, engines that burn fuels … and anything else.

Solving problems

In some situations, you can think in terms of either energy or force. For example, when trying to improve vehicle safety in the event of a crash, you could calculate the energy absorbed in the collision, or calculate the forces acting on the vehicle’s occupants.

Physicists are resourceful and will draw on whatever thinking tools help them understand a particular situation. They prefer to understand things quantitatively.

One important aspect of students’ growing understanding of energy ideas involves sorting out the ideas of heat and temperature (hotness or coldness).

Kinetic theory describes the energy of an object as being due to the random motion of its molecules. If you give more energy to be shared out amongst the atoms and molecules of some piece of matter, it usually gets hotter. But ‘hotness’ is not energy. Something hot (like the surface of the Sun, or a flame in a gas cooker, rather easily gives up energy to cooler things (energy goes without help from hotter to cooler).

What counts is the average energy per particle, not the total energy stored. So hot objects have, as it were, very concentrated energy that easily spreads out and dilutes, warming other things. This is what lies behind talk about “heat is a form of energy”. It is best to refer, as soon as possible, to the sharing out of energy amongst the motion of all the particles.

Students will learn that all energy transfers involve some losses through energy dissipation. They deserve (and will understand) an explanation of how this happens, and not simply a dramatic conclusion about the Universe warming in some mysterious way.

In describing ways in which energy goes from one place to another, physicists distinguish between ‘heating’ and 'working’. Heating is the process whereby energy moves from one object to another, which is in contact with it, as a result of their temperature difference.

Compressing and expanding gases

If a gas is compressed by pushing a piston quickly into a cylinder, the gas grows hotter: all the energy transferred to the gas goes into energy of molecular motion. If the gas then cools back to the original temperature, it transfers energy to the surroundings until they reach the same temperature. This will make its pressure fall slightly too, but still the pressure will remain higher than it was before compression.

The compressed gas, back at room temperature, can still transfer energy to other things by pushing the piston out. But the energy which it now supplies will be taken from the gas by cooling it down below room temperature.

Work is done whenever a force moves something over a distance. You can calculate the energy transferred, or work done, by multiplying the force by the distance moved in the direction of the force.

Energy transferred = work done = force x distance moved in the direction of the force

When energy is transferred from energy stored chemically in muscles to energy in a raised load, or to energy stored elastically in a stretched spring, the energy transferred is a measure of how much work has been done.

Energy transferred = mgΔh

This second equation is illustrated by raising kilograms onto different height shelves. You can show that the equation is a good summary of what happens. It takes account of the mass, the height raised and whether the kilogram is raised on the Earth or the Moon.

The useful thing which you get from fuels by burning them is a transfer of energy, so that a load can be raised, or an object accelerated.

However, not all the energy available does a useful job. If you lift a lot of bricks, you can get too hot. As well as transferring energy to the raised bricks, some of the energy in your muscles warms you up. The transfer of energy is not 100% efficient and not all the energy transferred is represented by mgh. Nor do you know how much total energy is stored gravitationally. You can only calculate energy that is transferred.

Concepts develop with steam engines

Humans first domesticated animals to do useful work and later found other ways of exploiting energy from natural sources, such as falling water and wind. But the abstract idea of an ‘engine’ really developed with steam engines.

By the 1820s the concept of ‘work’ as mechanical effect had been introduced into discussions about what are now called power technologies. Early on, a major use of steam engines was pumping water out of mines. Manufacturers such as Boulton & Watt persuaded mine owners in Cornwall to buy a steam engine in place of their pit ponies, by comparing the amount of work each could do.

Watt went even further, developing the concept of rate of working, or power, with his steam engines described in ‘horsepower’. Steam engines enabled the output of many Cornish mines to quadruple.

An analogy to use when teaching about energy transfers

Consider two bank accounts. If I transfer a £1 cheque from my account to yours then my account goes down by £1 and yours will go up by £1. But a cheque is not cash of any kind. It is an instruction to my bank to pay out £1 into your account. We have to pay the banks for doing the job for us and so although my account falls by £1 yours may only gain 95p because you have to pay bank charges. It is also impossible in this transaction to know how much is stored in each account.

Pushing this analogy to its limits helps to show that whilst you can store real cash in the bank (the energy stored, for example, in a fuel + oxygen mixture), the cheque which passes between accounts is something different. The cheque is a means of transferring the cash value (the work done for example when a brick is raised). Work is energy being transferred.

A discussion by Jon Ogborn, emeritus professor of science education at the Institute of Education, London.

An intrinsic problem of teaching about energy at secondary level is that school science is obliged to try to run before it can walk. School biology and chemistry need to use the idea of energy before its physical meaning or its measurement in terms of force multiplied by displacement can be taught.

Teachers want and need to talk about the role energy plays in changes, but the idea that energy is conserved (first law of thermodynamics) is simply not enough to do the job. What they need are some ideas from the second law of thermodynamics.

It is no real surprise that the world is richer and more complicated than science textbooks make it appear. And it is no surprise that it takes a lot of skill, knowledge and creativity to find good ways to explain things simply to young people.

In the resource downloadable below, I offer a rough guide to the fundamental physics, using these subtitles:

• What is energy?
• Energy is conserved
• Energy amongst the molecules
• Free energy
• Is energy needed for a change to happen?

and concluding with

• Is there a better way to teach energy?