Avoid chains of energy

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.