Black body radiation constant

The Stefan-Boltzmann Law and Wien s Law for black body radiation have been unified into Planck s Law for black body radiation, from which Planck s constant was first introduced. Planck s analysis of the spectral distribution of black body radiation led him to an understanding of the quantisation of energy and radiation and the role of the photon in the theory of radiation. The precise law relates the intensity of the radiation at all wavelengths with the temperature and has the form ... 

The experimental value of the constant is 5.67 X 10 8 W-m 2k 4. A few years later, in 1893, Wilhelm Wien examined the shift in color of black-body radiation as the temperature increases and discovered that the wavelength corresponding to the maximum in the intensity, max, is inversely proportional to the temperature, Xmax °c I IT, and therefore that max X T is a constant (Fig. 1.6). This quantitative result is now called Wien s law and is normally written... 

The minimum (or critical) heat flux required to reach ignition (because temperature and heat flux can be correlated with the Stefan-Boltzmann constant and black-body radiation). 

Planck constant — To describe the spectral distribution of energy of black body radiation -> Planck made the ad hoc assumption that the radiant energy could exist only in discrete quanta which were proportional to the frequency E = hu with h = 6.62 6 0 6 93(11) x 10 - 34 Js. Before 2003 the accepted value was 6.6260755(40) x 10-34 Js = 4.1356692(12) x 10-15 eV s. The quantity h later was referred to as Planck s constant. 

Emissivity is numerically equal to absorptivity. As emissive power varies with wavelength, the ratio should be quoted at a particular wavelength for many materials. However, the emissive power is a constant fraction of the black body radiation, that is, the emissivity is constant. These materials are known as gray bodies. 

To conclude this introduction to quantum mechanics, it is interesting to note the omnipresence and the agglutinating role of Planck s constant. Indeed, if it was set equal to zero, all the construction which began with black-body radiation and the quantization of radiation energy, followed by the wave-matter duality and the Heisenberg principle. .. would fall down. In addition, the intrinsic angular momentum (spin) of some particles, including the electron, would be forced to be zero, with many consequences at the theoretical and practical levels. 

COMMENT. Planck s estimate of the constant h in his first paper of 1900 on black body radiation was 6.55 x 10-27 erg sec(1 erg = 10 7 J) which is remarkably close to the current value of 6.626 x 10-34 J s and is essentially the same as the value obtained above, Also from his analysis of the experimental data he... 

To determine Boltzmann s constant, and so Avogadro s number, from a quantitative study of black-body radiation. 

As the constant a = 5.72 x 10 Wm K ", the heat flux from heater at 673 K is 12kWm . The power spectrum of black-body radiation shifts to shorter wavelengths as the temperature of the body increases. For a heater at 673 K, most of the spectrum lies in the infrared region at wavelengths 2-5 p,m. Although some polymers are transparent in the visible region, all polymers strongly absorb in the infrared, which excites vibration of the covalently bonded atoms. Consequently, the radiation is absorbed in the surface layer of the polymer. As the polymer surface temperature rarely exceeds 200 °C, Eq. (5.7) shows that the losses from re-radiation are small. 

Wien s displacement law For a black body, r= constant, where Xm is the wavelength corresponding to the maximum radiation of energy and Tis the thermodynamic temperature of the body. Thus as the temperature rises the maximum of the spectral energy distribution curve is displaced towards the short-wavelength end of the spectrum. The law was stated by Wilhelm Wien (1864-1928). 

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