Bringing together two sets of constraints

Focusing on the learners:

Distinguishing–eliciting–connecting. How to:

• draw on everyday conversations about energy, linking these to scientific discourse
• draw on concerns about energy supply
• formalise the discourse about energy by connecting it to calculations

Teacher Tip: These are all related to findings about children's ideas from research. The teaching activities will provide some suggestions. So will colleagues, near and far.

Focusing on the physics:

Representing–noticing–recording. How to:

• focus conversations about resources on the numbers
• connect societal concerns with scientific insights
• focus on the physical constraints on action revealed by energy calculations

Teacher Tip: Connecting what is experienced with what is written and drawn is essential to making sense of the connections between the theoretical world of physics and the lived-in world of the children. Don't forget to exemplify this action.

Coordinating teaching

It is very helpful to find out what your geography colleagues are teaching before starting the work on energy resources, as there is likely to be a fair overlap in the curriculum at this stage. Because of this we have concentrated on how the multiple energy resources that humans use are related to the scientific description in terms of energy stores and pathways. It would be helpful to come to an agreement with geography colleagues about how much they are going to cover in their treatment of alternatives in the energy economy.

A scheme to use

Thinking about the teaching

When using these different terms, it might be helpful to have this kind of scheme in mind.

Describing pathways

Thinking about the teaching

Pathways describe the ways in which energy is shifting into and out of stores as they are being filled and emptied. The pathway allows us to think about accumulations of energy that has been shifted (or the rate at which the energy is shifting) and tells us a little about the mechanism by which this occurs.

There is a clear difference between energy stores and pathways and this needs to be emphasised in your teaching. Consider the example of stretching a rubber band:

Here the elastic store associated with the band is filled by mechanical working (the pathway) as you pull on the band.

The full energy story is told using both stores and pathways.

Keeping it simple

In presenting these various energy descriptions of familiar processes, we have been careful to study one process at a time, moving from one snapshot of a system to another. This restricts attention to analysing the energy shift from store A to store B or perhaps from store A to store C. We recommend that you follow this practice and are not drawn into constructing long energy chains. Doing so can over-complicate the simple accountancy of the energy system and may lead to situations where stores are introduced for which there is no change. Here we discuss two examples where you might be tempted to consider intermediate stages.

The first example consists of an electric motor being used to lift a mass.

The energy description involves the quantity of energy removed from the chemical store (associated with the cell) as a result of the reaction of the chemicals in the cell. This energy is shifted to the gravitational store of the mass (in the Earth's gravitational field) as a result of the force acting on the mass through the specified distance.

The speed at which the mass travels upwards is not important to these changes, since the energy gained by the mass is fixed (as it is raised through a fixed distance). We think that you should always try to keep these energy descriptions as simple as possible and focus on the snapshots at the beginning and the end. This may well be in contrast to existing approaches:

Commonly used approach:

There is an energy transfer: Chemical energy (battery) to … Electrical energy (motor) to … Kinetic energy (mass) to … Gravitational energy (mass)

Recommended approach:

Energy is shifted from the chemical store (of the cell) to the gravitational store (of the mass).

Note that there are two differences in the approaches. Firstly, according to the recommended approach, electrical stores do not exist (although electromagnetic stores do exist – but these are for static situations where charged particles or magnets are held apart) so there is no electrical energy term. Secondly, kinetic stores have no part to play in the description simply because there is no change in the quantity of energy in that store (the mass rises steadily and so the energy in the kinetic store is constant). In other words we do not have the situation where one store is being emptied and another filled. The kinetic store does not change.

The only development which might be made to this recommended description is to recognise that not all of the energy shifted from the chemical store will end up in the gravitational store, so justifying adding a thermal store (of the surroundings) to which some of the energy is shifted.

Water runs through a turbine to run a generator and light a lamp

In this second example, you might be tempted to consider the kinetic energy of the water – but think again! The tube leading to the turbine is the same diameter as the tube leading from the turbine. Unless there is a build-up of water in the turbine, the flow rate to the turbine must be the same as the flow rate from the turbine. The same mass of water per second come in as goes out, and at the same speed. In other words, the energy in the kinetic store associated with the movement of the water does not change. The simple description of the system is that energy is shifted from the gravitational store to the thermal store.

The best advice for you is to concentrate on the initial and final states and to identify the stores that are being emptied and filled.

One step at a time

When analysing more complex systems, such as what happens with trophic levels in ecosystems or in multiple stage chemical reactions, the same advice applies. You may need to consider several steps, but in order to do the calculations, it is best to deal with one step at a time rather than trying to do a calculation halfway through each step, which is what is implied by drawing a chain. To do the calculation for each state, you need a snapshot of the system in that state, so starting or ending an analysis of the energy shifted from one store to another.

Refining energy descriptions for three roller coasters

Energy calculations are a way of determining what's possible and what's not. To determine if a process is possible then you need to define the process rather carefully, by at least fixing the start and end points. That's the minimum: you cannot even start an energy description without such a precise description. As you can perhaps imagine, this may not be enough to say what could happen, although it will be enough to determine what cannot happen.

To develop an energy description you compare a starting snapshot with a finishing snapshot: in both cases having in mind calculating the energy in the stores. If the energy in the stores is lower at the end of the process than at the beginning, then the process might happen. If the energy in the stores at the end is higher than at the beginning, then the process certainly will not happen.

Here are three processes to think about, where a ball rolls along a smooth track. Just from the energy snapshots you can tell the first is impossible, because energy is not conserved. The other two might be, but you cannot be sure. In none of the cases do the calculations of changes in the energy in the stores tell you what will happen.

Further information on the second case suggests that it will not happen, but the third could. (At least on large scales: for small objects, in the counter-intuitive world of the quantum, such possibilities are routine). It seems that you'll need to modify the snapshots to determine the differences between the second and third possibilities, that is to develop a multi-step energy description.

Roller coasters with humps

This description of the third coaster is best done in two stages. That we have to try again, to modify a description, should not come as any kind of surprise, nor count as any kind of failure in the approach. Neither history nor current experience of physics suggests that there are algorithms for developing successful descriptions of physical processes – it's one of the empirical sciences.

We'd suggest the new analysis takes the top of the hill as a break point: So the first energy description is from the original start point to the top of the hill: the second from the top of the hill to the original end point.

Roller coasters and activation energy

So it appears that we have to supply some energy from somewhere in order to release the final bonanza. There is an activation barrier to overcome. Although we have modelled this physically, this same situation is common in chemistry, where the energy in the chemical store associated with the reactants is commonly greater than the energy in the chemical store associated with the products, and yet the reaction still does happen until we've pushed it over some barrier, by supplying some energy. This is just like the roller coaster in the example we've just looked at: the energy needed to allow the reaction to happen, the difference between the start and end of the first phase of the analysis is called the activation energy; the intermediate state, corrresponding to the top of the hill, the activated state.

Chain flows in biology

An account of an ecosystem often includes a measure of the flow of energy through a system. This can include arrows where the thickness of the arrow shows the quantity of energy shifted from store to store. This is helpful for the account that we have suggested. Often these changes are linked to what happens per square metre of an ecosystem over a year, that is, the energy change is found (a painstaking task) for this length of time and for this area. The calculations are often done for a particular trophic level in an ecosystem, say the primary consumers. To do this you must, as we have been suggesting, choose a process very carefully, defining what you are prepared to measure over both time and space. Then you can produce a description in terms of the stores of energy.

Notice the limited range of stores (either chemical or thermal). You might then step up a level to concentrate on the secondary consumers (here we're imagining a food web where there are no tertiary consumers), or down a level to consider the producers (and here of course, you find out that what is unique is their ability to deplete a new kind of store not available to consumers). Note that each diagram is drawn to a very different scale.

Energy running out

Wrong Track: There is less energy at the end than at the beginning. You can do less.

Right Lines: Energy can only be shifted from one store to another. If you have chosen what to study carefully, the same quantity of energy is there at any time, it is just shared out differently amongst the stores.

Conservation of energy

Thinking about the teaching

Sometimes the conservation of energy conflicts with our intuition that things get used up and lost to further use. This is understandable in the case of burning something like methylated spirits in air to warm up some water. After the process, the meths has obviously gone. We cannot use it again. So just how does conservation apply here?

Perhaps the best approach in such cases is to emphasise, time and again, the spreading out of the energy amongst many small stores. In the case of the meths, the water is warmed, but so is the air, the container for the water and the burner. In addition, some radiation is emitted, which could end up warming something far away. Of course the collective name for all of these actions is dissipation. Rather than just providing this label, it may be more convincing for children to explicitly search out all of the stores that are filled (some only a small amount) as they track the energy leaving the original chemical store.

A car travelling on the motorway at constant speed – what else?

Wrong Track: That car is travelling along the motorway, so it's kinetic store must be changing.

Right Lines: The car is travelling at constant speed. The energy in the kinetic store only changes if there is a change in speed. There is no change in speed, so we do not need to concern ourselves with a kinetic store.

Keeping the description as simple as possible

Thinking about the learning

It is all too easy to make descriptions more complicated than they need to be. The idea with energy is to develop a simple abstract description that gives us an overview. So here comes eraser is all important – do not include anything that is not essential or useful. To be useful it needs to be possible to calculate a change in the energy in a store.

Thinking about the teaching

In dynamic equilibria, there may be many changes, but some things will be constant. One of the things which may be constant is the energy in a store. Keep an special eye out for these stores, so that you do not include them in any description of the energy in the stores for the initial or for the final snapshot.

The case of something moving at constant speed is one such example which is commonly used. But there are others – for example, if an animal is simply maintaining its body mass then the energy in the chemical store associated with that biomass does not change. There are other changes and these are important: the chemical store associated with the foodstuff that the animal consumes will be depleted; the chemical store associated the detritus excreted by that animal will also change; the thermal store associated with the environment will also change, as the animal warms its environment.

Teacher Tip: Think about a living, grown hen as being like a car journey from Hatfield to Birmingham. Start point: yesterday; end point: today. In both cases, a chemical store is emptied and the internal store of the environment is filled up. The chemical store of the hen is constant and not relevant to the calculation: nor is the energy in the kinetic store associated with the car.

Teacher Tip: Growing a hen from a fertilised egg is altogether different. Now, of course, a chemical store associated with the hen does get filled. As does the internal store associated with the environment and the chemical store of the detritus. The chemical store of the hen is measured in biology as the biomass. (If you're focusing on a biological description, from this point onwards, it seems closer to the physical realities not to mention energy but just refer to biomass.)

There's a good chance you could improve your teaching if you were to:

Try these

• linking the discussion about the depletion of resources to the ideas of stores
• linking the distinction between renewable and non-renewable to human concerns and timescales
• clearly distinguishing between stores (joules) and pathways (watts)

Teacher Tip: Work through the Physics Narrative to find these lines of thinking worked out and then look in the Teaching Approaches for some examples of activities.

Avoid these

• conflating rates of power in pathways with stores of energy
• connecting together more than two stores into a chain, eg kinetic  →  thermal  →  gravitational
• talking about energy being lost, running out or wasted
• developing complicated descriptions of cases of dynamic equilibrium

Teacher Tip: These difficulties are distilled from: the research findings; the practice of well-connected teachers with expertise; issues intrinsic to representing the physics well.