PLANCK’S LAW AND WIEN’S DISPLACEMENT LAW

Radiation in the region of the electromagnetic spectrum from approximately 0.2 to ap­proximately ЮОО /mi is called thermal radiation and is emitted by all substances by virtue of their temperature. The wavelength distribution of radiation emitted by a black­body is given by Planck’s law[17] [18] (Richtmyer and Kennard, 1947):

£ „__________ *nhCj__ , (34J

w Аі[ехр{/іС0/ЛіГ) – I] 1 *

where h is Planck’s constant, and к is Boltzmann’s constant. The groups 2-nhC* and iiCJk are often called Planck’s first and second radiation constants and given the symbols C, and C3. respectively.1 Recommended values are Ct = 3.7405 X 10s W /шИ/m1 and C, = і4.387.8 fxm K.

It is also of interest to know the wavelength corresponding to the maximum Intensity of blackbody radiation. By differentiating Planck’s distribution and equating to zero, the wavelength corresponding to the maximum of the distribution can be derived. This leads to Wien’s displacement law, which can be written as

ЛІЙМГ = 2897.8 /мп К (3.4.2)

Planck’s law and Wien’s displacement law are illustrated in Figure 3.4.1, which shows spectral radiation distribution for blackbody radiation from sources at 6000, 1000, and 400 K. The shape of the distribution and the displacement of the wavelength of maximum intensity arc clearly shown. Note that 6000 К represents an approximation of the surface temperature of the sun so the distribution shown for that temperature is an

image266

Figure 3.4.1 Spectral disiribution of blackbody radiation.

approximation of tlie distribution of solar radiation outside the earth’s atmosphere. The other two temperatures are representative of those encountered in low – and hlgh – icmperature solar-heated surfaces.

Tire same information shown in Figure 3.4.1 has been replotted on a normalized linear scale in Figure 3.4.2. The ordinate on this figure, which ranges from 0 to I, is the ratio of the spectral emissive power to the maximum value at the same temperature. This clearly shows the wavelength division between a 6000 К source and lower temperature sources at 1000 and 400 K.

Updated: August 4, 2015 — 3:31 am