S1C9: Radiant Energy & Heat

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a) Electromagnetic radiations

In the preceding chapters, we explored the nature and processes of energy and force fields in a localized area, around and near their source. However, energy can also travel away from the source, propagating as waves, in which case it is called radiant energy of which there are two forms: electromagnetic radiation (EMR) or gravitational radiation. I will only touch briefly on the latter in the last section, just for the sake of knowledge, because it is extremely difficult to observe and we are not yet in a position to harvest this type of energy for any practical use other than for cosmological research.

In Section 6.d we spoke about energy conservation and how, in an isolated system, the form of energy could change over time but not its quantity. In fact, this goes back to the definition of an isolated system as a system that experiences neither an exchange of matter nor of energy. By opposition, in an open system both types of exchanges can take place and radiant energy is one of the main avenues of energy transfer out or into the system. For the time being, in keeping with the classical electrodynamics view, EMR will be described as waves and their behaviour explained accordingly but, in the upcoming section titled “wave-particle duality”, I will also spend time on the alternative perspective of EMR as streams of photons, after having the courtesy of properly introducing this particle.

In the classical view, as we have seen in Section 8.c, charged particles create an electric field while their movement creates a magnetic field, that was in Section 8.e. There is a third scenario: the acceleration of a charged particle. Such an acceleration creates an electromagnetic wave, a coupling of electric and magnetic fields travelling outward. If the charged particle undergoes accelerations by being made to oscillate at frequency “f” (expressed in Hz), then the frequency of the EM wave is also f and it oscillates in a direction orthogonal to its line of motion – technically, this is called a transverse wave. Unlike mechanical waves such as sound or water waves whose transmission relies on molecules bumping into each other, EM waves do not require a medium to propagate and can therefore travel infinite distances through space. And so we can see distant galaxies.

What do I mean by “see”? Exactly what the word means because the light we perceive is electromagnetic radiation. And in physics, the radio waves used for broadcasting are also light; they just fall at an end of the light spectrum that is beyond the visible part. Let’s shed some light on this.

The electromagnetic spectrum designates the entire range of EMR, it is generally arranged in increasing order of wavelength and decreasing order of frequency. The wavelength, noted lambda “λ“, is the distance between two points with the same phase, for example between the crests of two successive waves. The longer the wavelength, the lower the frequency, which makes intuitive sense since frequency can be thought as a form of density, in time. The longer the spatial separation between the phases, the more time separates them, the lower the frequency. The relationship between wavelength and frequency is simply: λ = v/f where “v” is the phase speed, which depends on the medium through which the wave is travelling. In a vacuum, v is the speed of light (approx. 300,000km/s) so the wavelength of a wave with a frequency of 10MHz is about 30m (3×10⁸/10⁷). For a sound wave propagating through the air, at ordinary pressure and 20°C temperature, the speed of sound is 343m/s so a 1kHz frequency translates into a 34cm wavelength and when you hear the sound of thunder you know that it takes about 3 seconds to travel 1 kilometre so you can roughly estimate its distance simply by counting in your head. So you know, the range of audible frequencies for humans extends from 20Hz to 20kHz and some dog species can hear up to 60kHz frequencies. The difference is not a quirk of nature, just the way our respective auditory systems evolved based on the needs and environment of each species.

By the way, the reason radio waves are the preferred frequency for telecommunications on the planet owes to their propagation properties: the longer wavelength tend not to be absorbed in the atmosphere and can even travel through many materials, including buildings. Not so with the likes of X rays but their very small wavelength makes them useful for other applications such as X-ray microscopy or X-ray crystallography, which is used to determine the atomic structure of crystals.

The diagram enclosed below shows the EM spectrum on a logarithmic scale, from the super high intensity gamma rays through X rays, UV, the visible spectrum of light, infra-red, microwaves, and all the way until radio waves with long wavelength. Startingly, the visible spectrum only occupies a very narrow bandwidth, between 400 and 800 terahertz (1×10¹²), which translates into wavelengths below one micrometre (1×10^-6). In the visible spectrum section of this diagram you will recognize the lights of the rainbow, from violet to red.

Figure 7: Electromagnetic spectrum

Credit: by Zedh and Gringer on Wikipedia (CC BY-SA 3.0)

There would be plenty to say and explain about the physical processes leading to the formation of rainbows and generally about the interaction of light and matter but that would lead us astray from the topic of energy. For the readers so inclined, I have included a link to the Wikipedia entry on the subject of optics at the end of this chapter.

Likewise, there would be plenty to say about polarization, a property of transverse waves such as the electromagnetic ones. Essentially, polarization is a consistent oscillation behaviour of light (or EM waves) in relation with its direction of travel. When the fields oscillate in phase this is termed linear polarization and, when there is a phase difference, this will create an elliptical movement, or a circular one if the phase difference is exactly 90°. I mention polarization because this is another instance where there is a quantum take on the classical electrodynamics, namely that it is caused by the spin characteristics of the stream of photons within the wave.

b) The photon and wave-particle duality

Onto the photon then. This elementary particle has been mentioned a few times in passing. Mostly as being absorbed or emitted, but I am yet to dedicate the description and explanation it deserves. Now is the time.

In the Standard Model theory, the photon is classified as the boson mediating the electromagnetic interaction. It has no electric charge and has also been proven to be massless, the only elementary particle with such property, although the gluon which mediates the strong interaction is also thought not to have mass but this can’t be measured experimentally. Accordingly, photons travel at the speed of light in a vacuum and so do the EM waves they form.

The third important property of the photon is the proportional relationship between the energy it carries and its electromagnetic frequency. The formula is E=h.f where “h” is the Planck constant expressed in electronvolt per hertz (or joule per hertz). Generally, a photon’s energy is measured in electronvolt (eV) – refer to Section 6.e for more details on how to think about this unit. Since frequency is speed of light divided by the wavelength, then we can compute the energy of photons as long as we know either their frequency or wavelength.

This relatively simple formula, coupled with the idea that electromagnetic waves are formed by streams of photons leads directly to an important consequence: energy comes in discrete units. This aspect, the ability to quantify the properties of a system such as its energy or momentum to discrete values, is what distinguishes a quantum system from a classic one where those two properties show continuity in measurements, instead of coming in packets.

One more thing to close the loop on the formation of electromagnetic waves. When an electron (or other charged particle) moves from a high energy state back to a lower energy state, a photon is emitted carrying the difference in energy value – this is in keeping with the fact that energy can be transferred but is always conserved. This phenomenon occurs when the charged particles are made to oscillate and therefore undergo repeated accelerations, which ties in with the classical explanation we saw in the previous section, and it also clarifies why the energy levels of electrons can only have discrete values.

So far so good, right? Except, which is it – are the fundamental entities that make up our universe waves or particles? This is somehow disorienting because wave and particle mechanics differ in several respects; in particular a wave equation will yield continuous values over time and waves display interference when they are combined but their phases are not aligned – this is the principle of superposition of waves and it is an observable behaviour. As for particles, they are not subject to interference and have well-defined trajectories, a function of their velocities and starting position. Some of these characteristics cannot be reconciled and yet, entities like the photon or the electron can be modelled either as a wave or as a particle. Arguably the best-known evidence of this is the double-slit experiment which showed interference even though photons are detected to pass through one slit at a time – I have included a link to the relevant Wikipedia entry at the end. On the face of it this seems impossible and, of course, the contradiction lies with our thought process rather than in the inner mechanics of nature. This is where the concept of wave-particle duality comes in.

It is actually simple, even though the implications might not be. Wave-particle duality means that these entities we call electrons, photons or even atoms display wave-like properties as well as particle-like properties but, since one entity cannot be at the same time a wave and a particle, they are neither. They are something else. The contradiction therefore only arises when we try to fit those objects within one of the two abstractions we have developed: waves and particles. This struggle to represent an electron or a photon in our mind’s eye is not a failure of imagination, it is a failure of conceptualization, of mental representation. Understandable, really, because it is a hard endeavour to represent something we can’t physically perceive, like an extra dimension.

We are now on the cusp of quantum mechanics, a theory dealing with the sub-atomic scale with a different approach from classical mechanics, and there are so many fascinating aspects to it such as the uncertainty principle and the question marks surrounding causality. I have however decided not to dive in the topic for a few reasons: it would be a marked digression from the theme of this chapter, which is radiant energy and heat, it deserves at least an entire chapter, it is highly mathematical, and even if the predictions accord dramatically well with experimental results, much of it is still highly speculative. Also, it is bewildering. As Niels Bohr, one of the fathers of quantum physics stated about a century ago: “If you can fathom quantum mechanics without getting dizzy, you don’t get it”.

c) Thermal radiation and heat

Onto heat then. This is not a non-sequitur because thermal radiation is a form of EM radiation and is one of the three mechanisms of heat transfer. This will become clearer and hopefully even obvious after the term is explained.

In Chapter 6, several references to isolated systems were made and thermal energy was even briefly defined in Section 6.c. The system I referred to back then could have been called thermodynamic system, meaning it can comprise both matter and radiations that are deemed to be separate from their environment. In an isolated system there is no energy transfer from or toward the environment while in a closed system there can be an exchange of energy and in an open system there can be both a flow of energy and matter. The energy transfer can take place as work or as heat. Work, as we have seen previously, is done by the application of forces. As for heat, this type of energy transfer takes place when there is a difference in temperature between systems. This naturally begs the question of what temperature is.

You would recall kinetic energy relates to the motion of a body; in a given system, the temperature of this system reflects the amount of vibration and collisions of the bodies within this system: it is the measure of its average kinetic energy. When the amount of vibration is at the minimum and heat can no longer be transferred away from a system, its temperature is absolute zero. This is a defined term and the Kelvin temperature scale has been aligned to it so that it is equal to 0 kelvin. On the Celsius scale it is approximately -273.15 degrees. The lower the temperature, the lower the kinetic energy in the system and the more likely the drop through phase transitions of matter from gas to liquid and then to solid (refer to Section 2.e for explanation and descriptions of states of matter and phase transitions).

Unsurprisingly, the quantum of motion in a system impacts other processes such as electrical conductivity, the rate at which chemical reactions take place and even the speed of sound because as the temperature increases so does the speed of the molecules in the air so, all else being equal, they can carry the sound wave faster through collisions.

Going back to radiation, when electromagnetic radiations are generated by thermal motion, they can effectively be described as a form of heat transfer. In this case they are called thermal radiation, a phenomenon we are extremely familiar with since this is how we benefit from heat transfer from the distant Sun while the incandescence of the sun or even that of the filament of a light bulb corresponds to the visible spectrum of these heat-generated radiations.

Radiant heating is also used in the heating devices of our homes and commercial buildings and rely on the perception of temperature on our skin as the radiation reaches us, not on the warming of the air in between through convection or on the conduction of this heat through intermediary materials.

d) Thermal conduction and convection

Together with radiation, conduction and convection represent the three forms of heat transfer. Unlike radiation which doesn’t require a medium since the waves can propagate in a vacuum, conduction is perhaps the easiest to understand since it involves a transfer of heat via a static medium: the atoms and molecules of the system with a high temperature are highly agitated and will collide with the relatively calmer ones in a cooler system, thereby transferring some kinetic energy along the way. This happens incrementally at the microscopic level and only stops when the systems end up with the same temperature. Think of it as the lowest energy state, the one with the highest entropy that nature defaults to. Thanks to their strong inter-molecular interactions, the transmission of kinetic energy occurs much faster in solid than in gas, with liquid somewhere in between.

Convection on the other hand relies on the movement of a medium to transfer the heat, as opposed to travelling through the medium by conduction. And whereas conduction can be thought of at the microscopic scale, the phenomenon of convection takes place at a macroscopic level. The idea is actually not very complex: when a fluid (whether gas or liquid) is heated, the kinetic energy of the atoms and molecules within increase. If the boundaries are fixed then the pressure on these will increase but if it can expand then the boundaries will be pushed out. In that manner, when an area of a fluid is hotter than the surrounding area, it will expand. Accordingly, there will be less of those atoms and molecules per unit of volume, i.e. the relative density of the hot area will be lower than that of the cooler one. In an environment where there is a gravitational force, the denser part of the fluid will move down and the more buoyant one will move up – I have included a link to the Wikipedia article on buoyancy in the next section for those interested in the actual physics behind this phenomenon.

This differential in density creates the movement of fluids and results in wholesale heat transfer from one location to another. In most solid materials, neither the flow nor the diffusion that create differentials in density can occur, hence convection is a phenomenon taking place primarily in fluids. And it happens all around us. For instance, in Section 8.e I already mentioned convection in the Earth outer-core as being responsible for the flow of charged particles that create our planet’s magnetic field. And within the mantle, between the core and the crust of our planet, it is what drives plate tectonics.

Convection also eventuates in oceans and the atmosphere. In oceans, it generates currents and can be caused by differentials in heat or salinity since both of these have an impact on density. As for convection in the atmosphere, it is involved in various weather phenomena such as wind and the formation of clouds when hot air loaded with moisture rises through cooler air and the water vapor condensates.

Finally, let’s recap the various heat transfer mechanisms using cooking techniques as an example: we have microwaves relying on radiation, a frying pan making use of conduction and an electric oven will leverage both radiation and convection with the flow of air being ensured by a fan. In the case of a heater, all three techniques can be used as well: radiant heaters can nowadays be commonly found on outdoor terraces of cafes and restaurants, fans and other methods of air circulation can transfer heat by convection and a fireplace will primarily rely on radiation though some significant amount of heat will be lost up the chimney by convection.

e) Trivia – Gravitational waves

As promised at the outset of this chapter, a quick word on gravitational radiation, the second type of radiant energy. Somewhat similarly to the acceleration of charged particles producing electromagnetic waves, the motion of gravitating masses was predicted to generate gravitational waves travelling at the speed of light in a vacuum. This hypothesis did fit within Einstein’s theory of relativity and can be construed as “ripples in spacetime”, something classical mechanics would not accommodate of course since space and time are not linked dimensions in that framework and the interaction of gravitational forces was thought to be instantaneous.

Starting in the 1970s, there were some indirect observations of energy decay in far-off cosmical objects that closely matched the predictions of the hypotheses about gravitational waves. Eventually, these were recorded directly by LIGO, the Laser Interferometer Gravitational-Wave Observatory, in 2015 only two days after its improved detectors came online. The sensitivity of the set up consisting of 2 sets of two 4km-long vacuum tubes arranged in a L-shape located 3000kms apart is stupendous: it can detect changes in length, distortions created by the ripples in spacetime, of a small fraction of the charge diameter of a proton. To quote from the Ligo website, “At its most sensitive state, LIGO will be able to detect a change in distance between its mirrors 1/10,000th the width of a proton! This is equivalent to measuring the distance to the nearest star (some 4.2 light years away) to an accuracy smaller than the width of a human hair”.

Unarguably, this is big science. The first detection is thought to originate from the collision of two black holes, 1.4 billion light years away, and since then there have been many more detections.

As a closing remark, considering the weakness of the energy contained in the waves when they reach us, it is very doubtful this type of energy can be harvested in a manner that is remotely economical so the interest here is purely scientific, potentially peering in the early days of the universe to try and support or disprove cosmological hypotheses.

a) Electromagnetic radiations

b) The photon and wave-particle duality

c) Thermal radiation and heat

d) Thermal conduction and convection

e) Trivia – Gravitational waves

f) Further reading (S1C9)