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Radiation

Even though radiation may be the least familiar of the forms of heat transfer it is actually the simplest to understand because it always follows relatively simple mathematical rules. Because it is the only method that works in the vacuum of space it is also the most important means of transporting heat energy in the Universe!

What is ‘Radiation’?

All radiation, including the ‘thermal radiation’ covered here is just energy carried by photons, packets of light of various wavelengths. Each photon carries a fixed amount of energy:

Equation

Where h is Planck’s Constant = 6.63 x 10-34 J s and f is the frequency of the light.

How does Radiation Occur?

Whenever a charged particle, such as an electron is accelerated then it will radiate energy. This can be put to use in equipment such as radio transmitters and microwave ovens in order to emit a tightly defined, tuned radiation. In hot objects though the accelerations can be thought of as coming from the random motion of the electrons near the surface of the hot object. This is what is called a ‘classical’ explanation as it treats the electrons as if they were small, charged balls. A fuller explanation requires the use of quantum mechanics and is best left to be dealt with in a university physics course.

The thing that distinguishes ‘thermal radiation’ from other sources is its spectrum. Its shape follows a fairy complicated mathematical form that you are unlikely to need to understand before your university studies:

Equation

The important things are the shape, namely a steep curve up to a peak followed by a gradual exponential decline, together with some important facts about the way the shape depends on the temperature of the object:

Blackbody Radiation Curve

Equation

where T is the temperature in Kelvin.

Equation

where T is the temperature in Kelvin and sigma is a constant, equal to 5.67 x 10-8 J s-1 m-2 K-4. For the total power emitted by the entire object the equation becomes:

Equation

Equation

The implications of these observations are that for an object that is glowing purely due to its temperature:

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Even this is a simplification as it applies only to a ‘perfect’ radiator called a black body. Very close approximations to a perfect black body radiator include the heart of a coal fire and a high temperature furnace; looking into the depths of the coals you can see no detail of the individual coals, just a uniform colour dependant on the temperature.

The Sun, diameter 1.392 x 109 m, surface temperature 5778 K.

A section of a lightning strike, 1 cm2 and at a temperature of 30,000 K.

A circular pool of molten iron in a furnace of diameter 2.0 m and temperature 1550 °C.

The body of a survivor buried in the rubble after an earthquake. The temperature of the skin is 30 °C and 0.75 m2 is visible to a potential rescuer.

Emissivity

Very few objects are close to being perfect black body radiators. As a result they will radiate less energy than the ideal curve suggests. The emissivity epsilon is a measure of how far the object falls short of that ideal. You probably know that some things are better at absorbing radiation than others. We experience this if we go out in the sun in a black top, we would be much cooler if we were to wear a white top. The reverse also holds true, black objects are better radiators than white and the worst radiators are polished metal surfaces. This is why we wrap both jacket potatoes and exhausted hill walkers in metal foil, it reduces the amount of heat that they lose by radiation and so they stay warm.

A simple experiment can demonstrate this. Leslie’s cube is a hollow metal cube that contains either a heater or a tank for hot water. The four vertical faces of the cube have different finishes, usually matt black, matt white, dull aluminium and polished aluminium. When it is heated up you can place your hand or a radiation thermometer near (not on) the surfaces and it will quickly be obvious that the black surface radiates the most energy by far and the polished metal surface the least. In theory the emissivity of a material could vary between zero (a perfect reflector that as a result can never radiate at all) up to one (the ideal black body). In practice the values range from around 0.01 (highly polished gold) up to around 0.95 for many rough natural and man made surfaces. Because of this we should really use an amended version of the Stefan – Boltzmann Law:

Equation

And

Equation

Another simplification we have made is to assume that the object will not be receiving any energy in the form of radiation from the outside world. This is a fair assumption if we are studying the Sun (temperature 5800 K) radiating energy into deep space (background radiation temperature 2.73 K) but if we are using IR imaging equipment to look for a human body (306 K skin temperature) in a smoke filled room (298 K) the matter becomes rather important. When an object is surrounded by a warm or hot environment then we need to amend the equation again:

Equation

Detecting Radiation to Measuring Temperature

Different wavelengths of radiation need different types of detector. Radio waves for example are best detected with an antenna and a tuned circuit, a method that would never work for gamma rays. When we think of thermal radiation we tend to think of infrared radiation. This was first detected by William Herschel, accidentally, when he was studying the visible spectrum. A thermometer that was part of his experimental control suddenly increased its reading when it moved beyond the red end of the visible spectrum. An early method of measuring infrared radiation was the bolometer. In its most basic form it was a strip of platinum foil, blackened over a sooty candle flame. As infrared radiation fell on the strip its temperature would rise which would in turn increase its resistance. It was invented in 1878 by Samuel Pierpont Langley, which gave rise to the following lines:

Oh Langley devised the bolometer,

Which is really a kind of thermometer,

Which can measure the heat,

From a polar bear’s feet,

At a distance of half a kilometre.

Detecting radiation is the only practical method for measuring the temperatures of either very hot or inaccessible objects. In the first case any physical probe would melt in a very short time and in the second it would be impossible to position a probe anyway. For a long time the best method of measuring the temperature of, for example, a furnace would be a ‘disappearing filament optical pyrometer’. This is a little like a telescope equipped with filters and a small incandescent lamp.

Disapearing Filament Pyrometer

A Glassblower's Disappearing Filament Pyrometer

Disappearing Filament Pyrometer

Disappearing Filament Pyrometer Schematic

The optical pyrometer is pointed at the hot object. The red filter allows only a very narrow range of wavelengths to pass through the pyrometer so that only intensity rather than colour is judged by the user. The neutral density filters are set so that the object is seen to glow with a moderate intensity (this also determines the particular scale that the final reading needs to be made against). At this point there is no current passing through the lamp wire and so it is seen as a black silhouette against the bright, hot object. As the current is increased the wire gets hotter and so brighter. When the filament is the same brightness as the filtered hot object the filament will disappear and the effective temperature can be read off the meter on the pyrometer.

Disappearing Filament PyrometerDisappearing Filament PyrometerDisappearing Filament Pyrometer

Disappearing Filament Pyrometer: User's View.

This kind of device is still useful for measuring the temperature of small incandescent objects such as bulb filaments. However for most applications the disappearing filament optical pyrometer has been replaced by the radiation pyrometer. Instead of using the human eye to compare the brightness of a narrow strip of the visible spectrum a radiation pyrometer focuses the total radiation, both visible and infrared, on to an electronic detector. The signal from that detector can then be converted in to a temperature as long as the emissivity of the object is known. For most non metallic objects the emissivity can be taken to be approximately 0.95. They need to be adjusted though if the object is metallic and/or polished. An alternative and common trick is to place a small piece of black insulating tape on the object to be measured and then measure the temperature of the tape. Radiation pyrometers are even used now as clinical thermometers with the detector head being placed in the ear to measure the temperature of the tympanic membrane (ear drum).

Clinical Radiation Pyrometer

Clinical Radiation Pyrometer.

The intensity of radiation from an object falls off with the square of the distance to the detector. Why is it then that a radiation pyrometer (which has a very narrow angle of sensitivity) can be held at almost any distance from the object to be measured and still record the same temperature?

A radiation pyrometer is set to an emissivity of 0.95. It is then used to measure the temperature of a glass blower’s furnace (temperature 1100 °C to two significant figures) which approximates to a perfect black body. The glass blower then overlays the surface of a glass vase with gold foil and returns it to the annealing furnace (450 °C). What temperatures will the radiation pyrometer read from the working temperature furnace and the annealing gold vase? The emissivity of highly polished gold is approximately 0.01.

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