19.19 Radiation of heat

Before you read this, I suggest that you read post 19.9.

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We know that hot objects can emit electromagnetic radiation because sometimes they are “red hot”; then they emit red light – a form of electromagnetic radiation (post 19.9). The wavelength of emitted radiation shifts to shorter wavelengths (longer frequencies, post 19.9) as the temperature increases. We know this because hotter objects can be “white hot”; they emit a mixture of wavelengths (a mixture of colours) that combine to give white light. Since red light has the longest wavelength for visible light, these other wavelengths must be shorter (post 19.9).

This electromagnetic radiation can transmit heat. We can feel the heat from a red-hot object. If this heat were transmitted mainly by convection (usually the main mechanism for heat transfer in fluids, like air, post 19.18), a red-hot object would feel much hotter from above then from below (post 19.18). But it doesn’t. So, very hot objects can transmit heat in the form of electromagnetic radiation. When we absorb this radiation; its energy is dissipated inside us as heat; in much the same way as an object falling through a viscous fluid dissipates energy (post 17.17).

Light is not the only form of electromagnetic radiation that can transmit heat. For example, we often use microwaves to provide heat for cooking; microwaves are electromagnetic radiation with a longer wavelength then red light (post 19.9). Infra-red radiation has a wavelength between that of red light and microwaves (post 19.9). Since both light and microwaves can transmit heat, so can infra-red radiation.

graph

The picture above shows how the intensity of light emitted by an ideal radiator depends on the wavelength of the light and the temperature of the radiator. Two curves are shown: for objects at temperatures of 3000 K and 5000 K (post 16.34). Intensity is the energy of waves (post 19.8) emitted by unit area in unit time (measured in J.m-2.s-1 in the SI system – see posts 16.12 and 16.21). An ideal radiator emits and absorbs all wavelengths of electromagnetic radiation equally well; it is sometimes called a black body because it absorbs all wavelengths of light. This ideal radiator is an abstract concept, (like the simple harmonic oscillator in post 18.6), but it is possible to make something that behaves very nearly like an ideal radiator (in the same way that a pendulum behaves very like a simple harmonic oscillator) – allowing the experimental results above to be obtained.

Note that, at a given temperature, there is a maximum value for the wavelength emitted and that the position of this maximum shifts to a lower wavelength as the temperature increases.

You might expect that the shape of this curve could be predicted from the energy of a vibrating atom, since heat is simply atomic (or molecular) vibrations, post 16.35. People tried to do this in the nineteenth century and it didn’t work.

Then, in 1901 the German physicist Max Planck explained the shapes of these curves by assuming that light energy of frequency f could only be emitted in “packets” whose energy was hf where h is a constant whose value is 6.626 × 10-34 m2.kg.s-1. At the time, there was no justification for this assumption and it seemed to some people that Planck’s theory was no more than an empirical method for fitting the experimental curves – like the virial equations for real gases in post 19.2.

If you have read post 16.29, you will realise that Planck had discovered the quantum theory that Bohr used later to explain the energy of electrons in atoms. In this theory an oscillator of frequency f can gain or lose energy only in discrete amounts, hf, where h is called Planck’s constant. The discrete “packet” of energy is called a quantum (plural quanta). Because h is so small, quanta represent tiny amounts of energy when compared to the energy of an everyday oscillator, like a pendulum in post 18.6. So everyday objects appear able to have any amount of energy.

That people did not immediately see the importance of Planck’s idea may have led to his famous quote: “a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it”.

 

Related posts

19.18 Convection of heat
19.14 Fick’s law of diffusion and the conduction of heat
19.9 Electromagnetic radiation
16.35 Heat
16.34 Temperature

 

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