We all adore a Kia-OraAdvertising slogan for ‘Kia-Ora’ orange drink (c. 1985)
Energy is harder to define than you would think. Nobel laureate Richard Feynman defined ‘energy’ as
a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same. […] It is important to realize that in physics today, we have no knowledge of what energy is. […] It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas.Feynman Lectures on Physics, Vol 1, Lecture 4 Conservation of Energy (1963)
Current secondary school science teaching approaches to energy often picture energy as a ‘quasi-material substance’.
By ‘quasi-material substance’ we mean that ‘energy is like a material substance in how it behaves’ (Fairhurst 2021) and that some of its behaviours can be modelled as, say, an orange liquid (see IoP 2016).
And yet, sometimes these well-meaning (and, in my opinion, effective) approaches can draw some dismissive comments from some physicists.
What was the ‘Caloric Theory of Energy’?
To begin with, there was never a ‘Caloric Theory of Energy’ since the concept of energy had not been developed yet; but the Caloric Theory of Heat was an important step along the way.
Caloric was an invisible, weightless and self-repelling fluid that moved from hot objects to cold objects. Antoine Lavoisier (1743-1794) supposed that the total amount of caloric in the universe was constant: in other words, caloric was thought to be a conserved quantity.
Caloric was thought to be a form of ‘subtle matter’ that obeyed physical laws and yet was so attenuated that it was difficult to detect. This seems bizarre to our modern sensibilities and yet Caloric Theory did score some notable successes.
- Caloric explained how the volume of air changed with temperature. Cold air would absorb caloric and thus expand.
- The Carnot cycle which describes the maximum efficiency of a heat engine (i.e. a mechanical engine powered by heat) was developed by Sadi Carnot (1796-1832) on the basis of the Caloric Theory
Why Caloric Theory was replaced
It began with Count Rumford in 1798. He published some observations on the manufacturing process of cannons. Cannon barrels had to be drilled or bored out of solid cylinders of metal and this process generated huge quantities of heat. Rumford noted that cannons that had been previously bored produced as much heat as cannons that were being freshly bored for the first time. Caloric Theory suggested that this should not be the case as the older cannons would have lost a great deal of caloric from being previously drilled.
The fact that friction could seemingly generate limitless quantities of caloric strongly suggested that it was not a conserved quantity.
We now understand from the work James Prescott Joule (1818-1889) and Rudolf Clausius (1822-1888) that Caloric Theory had only a part of the big picture: it is energy that is the conserved quantity, not caloric or heat.
As Feynman puts it:
At the time when Carnot lived, the first law of thermodynamics, the conservation of energy, was not known. Carnot’s arguments [using the Caloric Theory] were so carefully drawn, however, that they are valid even though the first law was not known in his time!Feynman Lectures on Physics, Vol 1, Lecture 44 The Laws of Thermodynamics
In other words, the Caloric Theory is not automatically wrong in all respects — provided, that is, it is combined with the principle of conservation of energy, so that energy in general is conserved, and not just the energy associated with heat.
We now know, of course, that heat is not a form of attenuated ‘subtle matter’ but rather the detectable, cumulative result of the motion of quadrillions of microscopic particles. However, this is a complex picture for novice learners to absorb.
Caloric Theory as a bridging analogy
David Hammer (2000) argues persuasively that certain common student cognitive resources can serve as anchoring conceptions because they align well with physicists’ understanding of a particular topic. An anchoring conception helps to activate useful cognitive resources and a bridging analogy serves as a conduit to help students apply these resources in what is, initially, an unfamiliar situation.
The anchoring conception in this case is students’ understanding of the behaviour of liquids. The useful cognitive resources that are activated when this is brought into play include:
- the idea of spontaneous flow e.g. water flows downhill;
- the idea of measurement e.g. we can measure the volume of liquid in a container; and
- the idea of conservation of volume e.g. if we pour water from a jug into an empty cup then the total volume remains constant.
The bridging analogy which serves as a channel for students to apply these cognitive resources in the context of understanding energy transfers is the idea of ‘energy as a quasi-material substance’ (which can be considered as an iteration of the ‘adapted’ Caloric Theory which includes the conservation of energy).
The bridging analogy helps students understand that:
- energy can flow spontaneously e.g. from hot to cold;
- energy can be measured and quantified e.g. we can measure how much energy has been transferred into a thermal energy store; and
- energy does not appear or disappear: the total amount of energy in a closed system is constant.
Of course, a bridging analogy is not the last word but only the first step along the journey to a more complete understanding of the physics involved in energy transfers. However, I believe the ‘energy as a quasi-material substance’ analogy is very helpful in giving students a ‘sense of mechanism’ in their first encounters with this topic.
Teachers are, of course, free not to use this or other bridging analogies, but I hope that this post has persuaded even my more reluctant colleagues that they need a more substantive argument than a knee jerk ‘energy-as-substance = Caloric Theory = BAD’.
Fairhurst P. (2021), Best Evidence in Science Teaching: Teaching Energy. https://www.stem.org.uk/sites/default/files/pages/downloads/BEST_Article_Teaching%20energy.pdfhttps://www.stem.org.uk/sites/default/files/pages/downloads/BEST_Article_Teaching%20energy.pdf [Accessed April 2022]
Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics, 68(S1), S52-S59.
Institute of Physics (2016), Physics Narrative: Shifting Energy Between Stores. Available from https://spark.iop.org/collections/shifting-energy-between-stores-physics-narrative [Accessed April 2022]