Energy chain example: hydro-electric power station

This is the second post about situations in which we are drawn into including intermediate stores as part of an unhelpful chain or ladder. This post is a bit like an appendix, in which I will look at the example of a hydro-electric power station. So it is worth reading the overview first.

Here’s a quick summary anyway.

Quick summary

There are a number of situations for which there is a temptation to introduce chains of intermediate stages when a process is still occurring. They include:

1. Lifting a mass with a clockwork motor

2. A hydro-electric power station
3. Lighting a light bulb
4. Car making a journey
5. Heating a room
6. Pedalling a bike
7. A loudspeaker playing music

In the previous post, I looked at the example of the rising mass. In teaching schemes and assessments of the recent past (using types and transformations in the way that it had come to be used), student would be expected to reproduce an analysis something like:

elastic energy ⇒ kinetic energy (plus ‘sound energy’) ⇒ gravitational potential energy (plus ‘heat’)

I made the case for this chain being confusing and unphysical. And that spending time in teaching students to reproduce such chains is unhelpful because they are:

• Obscuring: drilling in the operational details of the labelling task hides (from learners) the interesting physical descriptions;
• Misleading: they paint an unhelpful picture of what is happening physically;
• Arbitrary: there is no physics-based reason for choosing one intermediate store over any others;
• Unenlightening: they shed no light on the physical processes nor do they provide any helpful tools for discussing or using energy ideas.
• Not relevant for any informative calculations.
• Ambiguous and confusing. there is no physics-based way for a student to reason their way to an expected answer.

I also suggested ways in which the analysis can be made more physical and educationally helpful. And they are to:

• Keep the energy analysis separate from the interesting physics stories;
• Identify start and end point that keep the energy analysis straightforward and relevant to the question.

I will endeavour to illustrate this approach with some of the other examples and hope to show that the resulting analyses are more helpful for learning good physics. First, let’s look at HEP. In the next post, I will look at electric circuits.

B. The hydro-electric power station

A good example for illustrating the ambiguous nature of chains is a hydro-electric power station.

Mechanisms and processes

The physics story (in brief) is: during a day, water drops from a high reservoir to a low one. In doing so, it turns turbines that drive generators, which generate an EMF. The output of the generator is connected to the National Grid. When someone switches on a kettle, the element draws a current from the national grid and its temperature rises as electrons are forced through its high resistance. The hot element then raises the temperature of the water by heating. Furthermore, during the time it takes to boil the kettle, a number of parts of the system (including the wires, the transformers and the water itself) will have got hot and raised the temperature of the surroundings by heating. Some bits will have been noisy; however, the sound waves will have been absorbed by the surroundings and raised their temperature a little.

All of the paragraph above is about mechanisms and processes. They may well need refining and each mechanism could be explored in more (or less) detail (of our choice when we tell the story). But we could probably agree on the physics.

Now let’s move to the energy analysis.

Energy story

First we need to choose start and end points that make the story simple and illustrative. I suggest taking a start point just before the kettle is switched on and an end point as the water boils.

The basic energy story is that

• the energy stored gravitationally at the HEP station is reduced (its water has ended up in a lower place)

• the energy stored thermally by the water in the kettle has increased (we have raised its temperature by electrical working).

You could show this change graphically:

We can embellish the story a little by including the idea that the hot water will raise the temperature of the surroundings (a little). Putting this into the language of stores, we can say:

• a gravitational store has emptied (a little)

• the energy in a thermal store (associated with the water in the kettle) has increased

• the energy in a thermal store (associated with the surroundings) has also increased.

Again, this can be represented nicely in a diagram:

By choosing start and end points that pass over all the intermediate considerations, we have, I suggest, avoided obscuring the physics, misleading students, confusing them with arbitrary choices and ambiguous decisions. Instead, the approach is enlightening and, amongst other things, prepares them for performing informative calculations using energy ideas.

By contrast, the approach from the recent past, using a chain of types of energy and conversions or transformations:

• obscures the story about processes and mechanisms. By attempting to mirror the physical processes, the chain of types is actually a distraction that covers them up and explains them away.

• misleads. There is a suggestions that, in order to boil the kettle, energy has had to flow through the system or change forms. Or somehow that the kinetic energy of the moving water carries energy from the reservoir to the turbines (it does not – instead it transmits a force that allows the system to transfer energy by mechanical working). Furthermore, this type of analysis has led to the need to invent and to present students with spurious ‘types’ of energy such as ‘sound energy’ and ‘electrical energy’ (and expect them to know about them).

• is arbitrary. The decisions about which ‘forms’ of energy to include has no basis in physics. Students might have included: kinetic energy (water), kinetic energy (turbines), sound energy, electrical energy and so on. The list would be (almost) endless. But probably have left out the energy stored elastically by the turbine blades, the energy stored by the water under pressure, the kinetic energy of the axles, coils etc. Importantly, the decision on which ones to include and exclude would be made purely by what an examiner or question setter was (arbitrarily) expecting – and not by any physical reasoning. Students would be coached in which ones to include through precedent and habit rather than physical reasoning.

• is ambiguous. Neither we, nor students, will arrive at a single agreeable result. Physics cannot tell us the exact sequence in which we string together the different ways in which energy is stored. In other words, producing the chain is a purely a rule-based labelling exercise rather than physics.

• sheds no light on either the physical processes or the energy story. Whilst it is true that the water is moving (as are the turbine blades) and that there is a sound and there is an electric current, all of these aspects are a part of the physics story and do not enlighten or inform the energy discussion. Nor does including them in an energy discussion help with their understanding of the physical processes.

• distracts from calculation. The energy analysis using start and end points is a preparation for a calculation. It is illuminating and interesting to calculate the changes to each of: the energy stored gravitationally, the energy stored thermally (by the kettle’s water), and how much energy has been transferred by electrical working. By contrast, the kinetic energy of the flowing water is constant and transient; it does not inform or illuminate any calculation. Nor does its value (at any time) relate to any of the interesting changes in the system.

• confuses through all of the above; especially through the picture it paints that energy is carried from one place to another by the constituents of the system – specifically the water flowing down the pipe. However, here is an oddity: when the water passes to the downside of the turbine, it will speed up. So, in fact, its kinetic energy will increase. So the picture of the water as an energy carrier is deeply flawed and confusing.

As I mentioned above, it is better to think of the HEP station as a transmitter of a force and to discuss energy being transferred through mechanical working rather than energy being carried by an intermediary.

A similar problem arises in electric circuits – where there is a temptation to paint a picture of charges carrying energy around the circuit (rather than energy being transferred by electrical working). I will follow this up in the next post.