Energy
Energy and Thermal Physics

Pathways

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Pathways

In the last two blogs, I have introduced the idea of ‘stores’ and, in the previous post, suggested that referring to eight stores will be helpful in discussions at Key Stage 3.

This post introduces the idea of pathways – the link between the physical processes and an energy analysis.

(Not too hard) work

Let’s try the three step approach on a clockwork motor lifting some masses.

We will choose a start point after the spring has been wound and an end point when the masses come to rest at the top.

Start point: there is an elastic store associated with the wound spring;

End point: there is a gravitational store associated with the masses. This store has filled as the elastic store has emptied. Some thermal stores have also filled a little.

  1. Observation: the spring unwinds and lifts the masses. The spring may have got a little warmer – though it would be hard to notice that in a small system.
  2. Discussion/Explanation (in brief – as ever, you can drill into the physical processes and mechanisms in as much detail as you choose): the coiled spring exerts an upwards force on the masses that is bigger than their weight. Therefore there is a net upwards force and they accelerate. They quickly reach a steady speed and the spring does work to raise them. It also does work against friction and air resistance and raises the temperature of the mechanism and surrounding air (ever so slightly).
  3. Energy analysis:

    We will choose a start point after the spring has been wound and an end point when the masses come to rest at the top.

    Start point: there is an elastic store associated with the wound spring;

    End point: there is a gravitational store associated with the masses. This store has filled as the elastic store has emptied. Some thermal stores have also filled a little.

The changes have come about through the spring doing work or working. To be more precise, we might call it ‘mechanical working’.

Points to note

  • It is worth trying to use the term ‘working’ rather than ‘doing work’ (at least some of the time) because it is clearly active and it will align with ‘heating’ later on.
  • There is (as ever) no role for a kinetic store in this analysis. The masses were moving (and that is discussed in step 2). But the movement is transient.
  • The initial temperature rises were brought about by working (as opposed to heating).
  • It is the springs that are working (not ‘elastic energy’). The job of working has to be done by a physical entity that exerts a force. It is not done by an energy store (or a type of energy). I.e. it is unhelpful to say something like: “the ‘elastic energy’ does work to raise the masses”.
  • Working is not a store. Or a ‘type’ of energy. We are going to call it a pathway.
  • The pathway has meaning in a physical discussion (step 2 above) or in an energy analysis (step 3).

Working a bit harder (electrically)

Now let’s get an electric circuit to do the same job.

  1. Observation: Attaching a cell to a motor drives the motor round and it lifts the weights. The motor gets hot (especially if it is run for a long time). And, eventually, the battery will run down.
  2. Discussion/Explanation: I will keep this discussion simple for the time being – it could get as involved as you like (there is nothing here that closes it down).

    The cell contains chemicals which produce an EMF across its terminals. The EMF can push charges around the circuit. These charges are already in the wires and form a continuous loop. As soon as the circuit is switched closed, the charges start to move and they do work in the motor to turn its shaft. Therefore the motor lifts the masses. The flow of charge is also part of a chemical reaction between the substances in the cell. This chemical reaction changes the useful chemicals into less useful products. Eventually, the reacting chemicals run out and the cell stops producing an EMF.

  3. Energy analysis:

    We will choose a start point before switching the circuit on and an end point after the masses have been raised.

    Start point: there is a chemical store associated with the cell.

    End point: the chemical store has emptied a bit and a gravitational store (associated with the masses) has been filled a bit; also, thermal stores associated with the wires, motor and air have been filled a little.

What is working now?

In this case, the working was done electrically by the cell and the circuit. So, it seems reasonable to say that the circuit was working electrically, i.e. this is a special case of working.


Points to note 

  • The circuit is working electrically rather than ‘carrying electrical energy’.
  • Electrical working is a pathway in the same way that mechanical working is a pathway.
  • The electric current is transient (in the same way that the movement of the masses is transient).
  • We do not need an electrical store in the analysis.

Let’s explore some of those points in more detail because I know some people feel uncomfortable that there is no electrical store – or equivalent of ‘electrical energy’ – in this analysis.

What happened to ‘electrical energy’?

I suggest that the usual analysis using the 9 types paradigm would have been something like:

chemical energy ⇒ electrical energy ⇒ gravitational energy

We are so used to this that many people are tempted to invent an ‘electrical store’ to use in the new analysis. However, although it is a difficult idea to drop, there are very good reasons why we don’t need such a term – and why the term ‘electrical energy’ is misleading in this context. They are:

  • There is no physical referent for ‘electrical energy’ in this circuit – i.e. there is no sense in which the moving charges store or ‘carry’ energy in the circuit.
  • There is certainly no way of calculating, at an instant, the ‘electrical energy’ associated with an electric current. The amount of work done depends on time – how long the circuit is switched on.
  • It is a spurious use of the term ‘electrical energy’. That term – like our electric/magnetic store – relates to the separation of one or more charges (or their position in an electric field). In circuits, we only need to invoke our electric store when we are considering capacitance (which is unlikely to happen at Key Stage 3).
  • The circuit is switched off at the start and end points. Therefore we don’t need to take the charges or their distribution into account. 

So, to summarise and emphasise, the charges are not storing or carrying electrical energy. Instead, they are enabling the circuit to do work (electrically) thanks to the fact that they form a continuous loop.

Being consistent

This analysis is consistent with our model of a continuous loop of moving charges in an operating electric circuit. It is also consistent with SPT’s rope-loop illustration of this model.

Heating as a pathway

To complete our toolkit, we need to introduce the idea of heating as a pathway. I’ll do this very briefly here and return to the idea in a subsequent post.

Heating is a well-defined idea in thermodynamics: it is the transfer of energy from an object at a higher temperature to one at a lower temperature. It is clearly helpful if we can use the term in a similar way at school level.

There are two mechanisms for enabling a hot object to heat a cooler one:

  • Heating by particles (when the bodies are in contact; AKA conduction)
  • Heating by radiation (when they are not in contact).

A cup of tea will heat its cooler surroundings by both conduction and radiation.

So, jumping straight to the energy analysis (for brevity)...

Start: there is thermal store associated with the tea

End: the tea’s thermal store has emptied and the thermal store of the surrounding has filled a bit. The pathways are heating by particles and heating by radiation.


Points to note

  • The word ‘heating’ makes it clear that this is a process (it is not a store). Nor does it sound like it might be a store.
  • The ‘ing’ formation makes it tally with working and electrical working.

Summary of pathways

We have discussed four pathways:

  • Working
  • Electrical working
  • Heating by particles
  • Heating by radiation

 

These will cover our needs and are discussed further in the SPT resources. Here are some points to note:

  • Pathways lead to energy stores being emptied and filled – i.e. they are the processes that bring about a change in the energy profile of a system.
  • They are not stores themselves because we cannot calculate the energy associated with them at an instant.
  • They bring about change by occurring over a period of time.
  • They fall into two pairs: working and heating.
  • They are consistent with the first law of thermodynamics – that there are two ways of changing the internal energy of a system: working and heating:  dU = dQ + dW

In summary – a complete toolkit (almost)

We now have a complete toolkit for discussing energy at Key Stage 3 – although I have skirted over some aspects here. It comprises:

  • The three step approach to discussion and analysis. Or, if you prefer, another way of distinguishing between the physical processes and the energy analysis.
  •  A set of stores associated with the ways that systems can store energy. It looks like we need just 8 of them.
  • A set of 4 pathways that describe how the physical processes lead to some stores being emptied and others being filled.

Note that this toolkit is not a model or a set of laws of physics – although it is consistent with some important physical laws and models – including some that we use at school.

Energy
appears in the relation ΔEΔt>ℏ/2 ΔQ=mcΔθ E=hf E ∝ A^2
has the special case Photon Energy
is used in analyses relating to Emission/Absorption Spectra Phase Change
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