1.3 planckian radiators and colour temperature

COMPILED BY TANVEER AHMED 1

PLANCKIAN RADIATORS AND COLOUR TEMPERATURE

spectral power distribution (SPD) curves of the heat/light source,


spectral power distribution (SPD) curves

When a coal fire is lit (or when the bar of an electric fire is

switched on), it first of all▪ glows a dull red, ▪ then orange-red, ▪ then yellow;

eventually it approaches the ‘white-hot’ stage as the temperature rises.

At the same time the total amount of energy emitted rises (the fire gets steadily hotter).


spectral power distribution (SPD) curves

The radiative power emitted by a heated body is best described by a plot showing the

variation across the electromagnetic spectrum of the Emittance

(for example, in watts per square metre) per unit wavelength.

Such curves are known as the spectral power distribution (SPD)

curves of the heat/light source, and Figure 1.5 illustrates

how these curves change in the visible region as the temperature of the heated body rises.


Planckian or black body radiator A Planckian or black body radiator is

an idealised radiation source consisting of a▪ heated enclosure from which radiation escapes

through an opening whose area is small▪ compared to the total internal surface area of

the enclosure (in practice approximated to by a

small hole in the side of a large furnace).


Planckian or black body radiator

The term ‘black body’ was originally used in recognition that

▪ such a model source would radiate energy perfectly▪ and conversely would absorb light perfectly, ▪ without reflecting any of it away, ▪ in the manner of an ideal black object.

Nowadays such a model source is referred to as an ideal, full or Planckian radiator.


Austrian physicist Josef Stefan 1879

The Austrian physicist Josef Stefan showed in 1879 that the total radiation emitted by such a heated body depended only on its temperature

and was independent of ▪ the nature of the material from which it was

constructed.


world’s leading theoretical and practical physicists

Considerable debate about the spectral distribution from these

▪ so-called black bodies ensued,

in which many of the world’s leading theoretical and practical physicists joined: these included

▪ Wien,▪ Jeans ▪ and Lord Rayleigh.


German physicist Max Planck (1900)

In 1900, however, the German physicist Max Planck developed a theoretical treatment that▪ correctly predicted the form of the spectral power distribution curves ▪ for different temperatures

(it took the support of Einstein in 1905 to convince the sceptics).

Planck’s breakthrough came through the assumption

that ▪ radiation was not emitted continuously▪ but only in small packets or quanta, ▪ With the energy of the quantum being directly proportional to the

frequency of the radiation involved


German physicist Max Planck (1900)

Planck used his now famous Eqn 1.5 to derive an expression for

▪ the spectral emittance ▪ from which the SPD curve of the source can be

calculated.

The Planckian radiation expression has the form of Eqn 1.7:


SPD curves for Planckian radiators

Some examples of the SPD curves for Planckian radiators at different temperatures based on Eqn 1.7 are shown in Figure 1.6.

To accommodate the large ranges of values involved, Figure 1.6 shows the power on a logarithmic scale

(note the units used) plotted against the wavelength in nm, also on a logarithmic scale,

and illustrates how at temperatures below 6000 K most of the energy is concentrated in the long-wavelength IR or heat region of the electromagnetic spectrum.

In fact the emission over the visible region is only a small part of the total emission for any of the curves shown.



The shape of the SPD curve across the visible region changes significantly,

however, from about 1000 K

at which the colour appearance of the emitted radiation is predominantly red

to 10, 000 K, at which it is bluish-white (Figure 1.7).

Between these two limits the colour changes

from red, through orange-red to yellowish-white and eventually to bluish-

white, as discussed above.



The closest approach to the ideal equi-energy (ideal white

light) source with constant emittance ▪ across the visible spectrum▪ occurs somewhere between 5000 and 6000

K. Thus we can associate the colour

appearance of the source with the temperature

▪ at which a Planckian radiator will give approximately the same colour appearance.


SPD curves for Planckian radiators The precise connection between

▪ colour temperature ▪ and Planckian radiator temperature▪ (and that of correlated colour temperature)

is best discussed through a plot of▪ the colour coordinates of the Planckian radiators on a suitable

CIE chromaticity diagram The typical 100 W domestic tungsten light

bulb has a ▪ colour temperature of about 2800 K.

That of a tungsten–halogen projector bulb ▪ is about 3100 K,

whilst that of average daylight from an overcast sky ▪ is about 6500 K.

1.3 planckian radiators and colour temperature

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