spectral power distribution (SPD) curves of the heat/light source,                   COMPILED BY TANVEER AHMED            ...
   When a coal fire is lit   (or when the bar of an electric fire is switched    on), it first of all       ▪ glows a du...
   The radiative power emitted by a    heated body     is best described by a plot showing the      variation across the...
   A Planckian or black body radiator is an    idealised radiation source consisting of a      ▪ heated enclosure from wh...
   The term ‘black body’ was originally used in    recognition that       ▪   such a model source would radiate energy pe...
   The Austrian physicist Josef Stefan showed    in 1879 that     the total radiation emitted     by such a heated body...
   Considerable debate about the spectral    distribution from these       ▪ so-called black bodies ensued,    in which ...
   In 1900, however, the German physicist Max Planck    developed a theoretical treatment that      ▪ correctly predicted...
   Planck used his now famous Eqn 1.5 to    derive an expression for       ▪ the spectral emittance       ▪ from which th...
   Some examples of the SPD curves for    Planckian radiators at different    temperatures based on Eqn 1.7 are shown    ...
 The shape of the SPD curve  across the visible region  changes significantly, however, from about 1000 K at which the ...
   The closest approach to the   ideal equi-energy (ideal white light) source    with constant emittance     ▪ across th...
   The precise connection between        ▪ colour temperature        ▪ and Planckian radiator temperature        ▪ (and t...
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1.3 planckian radiators and colour temperature

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1.3 planckian radiators and colour temperature

  1. 1. spectral power distribution (SPD) curves of the heat/light source, COMPILED BY TANVEER AHMED 1
  2. 2.  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). COMPILED BY TANVEER AHMED 2
  3. 3.  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. COMPILED BY TANVEER AHMED 3
  4. 4.  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). COMPILED BY TANVEER AHMED 4
  5. 5.  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. COMPILED BY TANVEER AHMED 5
  6. 6.  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. COMPILED BY TANVEER AHMED 6
  7. 7.  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. COMPILED BY TANVEER AHMED 7
  8. 8.  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 COMPILED BY TANVEER AHMED 8
  9. 9.  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: COMPILED BY TANVEER AHMED 9
  10. 10.  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. COMPILED BY TANVEER AHMED 10
  11. 11.  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. COMPILED BY TANVEER AHMED 11
  12. 12.  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. COMPILED BY TANVEER AHMED 12
  13. 13.  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. COMPILED BY TANVEER AHMED 13

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