Wiens law

In the late nineteenth century, Wien analyzed experimental data on blackbody radiation and found that the maximum of the blackbody radiation specti um shifts with the temperature according to the equation 

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The Planck formula suggests how to find numerical values of constants in Stefan-Boltzmann and Wien laws. In particular on integration of Kirchhoff s law on the whole frequency range one can arrive at the Stefan-Boltzmann formula. The constant in Wien s law b can be found by derivation of the Kirchhoff s function on frequency and equalizing it to zero. We hope that readers can carry out these calculations themselves. 

The Wien displacement law states that the wavelength of maximum emission, A , of a blackbody varies inversely with absolute temperature the product A T remains constant. When A is expressed in micrometers, the law becomes... 

Blackbody Emittance. Representative blackbody emittance (9,10), calculated as a power spectral density, is shown in Figure 2. The wavelength, X, of peak power density for a blackbody at temperature, T, is given by Wien s displacement law ... 

Radiometry. Radiometry is the measurement of radiant electromagnetic energy (17,18,134), considered herein to be the direct detection and spectroscopic analysis of ambient thermal emission, as distinguished from techniques in which the sample is actively probed. At any temperature above absolute zero, some molecules are in thermally populated excited levels, and transitions from these to the ground state radiate energy at characteristic frequencies. Erom Wien s displacement law, T = 2898 //m-K, the emission maximum at 300 K is near 10 fim in the mid-ir. This radiation occurs at just the energies of molecular rovibrational transitions, so thermal emission carries much the same information as an ir absorption spectmm. Detection of the emissions of remote thermal sources is the ultimate passive and noninvasive technique, requiring not even an optical probe of the sampled volume. 

The wavelength of maximum intensity is seen to be inversely proportional to the absolute temperature. The relation is known as Wien s displacement law = (2.898)(10 ) m K. This can be... 

Ratio Pyrometers The ratio pyrometer is also called the two-color pyrometer. Two different wavelengths are utilized for detecting the radiated signal. If one uses Wien s law for small values of XT, the detected signals from spectral radiant energy flux emitted at the wavelengths and 2 with emissivities and are... 

As seen in Eq. (17-1), the total radiation from a blackbody is dependent on the fourth power of ifs absolute temperature. The frequency of the maximum intensity of this radiation is also related to temperature through Wien s displacement law (derived from Planck s law) ... 

The sun radiates approximately as a blackbody, with an effective temperature of about 6000 K. The total solar flux is 3.9 x 10 W. Using Wien s law, it has been found that the frequency of maximum solar radiation intensity is 6.3 x 10 s (X = 0.48 /rm), which is in the visible part of the spectrum 99% of solar radiation occurs between the frequencies of 7.5 X 10 s (X = 4/um) and 2 x 10 s (X = 0.15/um) and about 50% in the visible region between 4.3 x 10 s (X = 0.7 /rm) and 7.5 X 10 s (X = 0.4 /Ltm). The intensity of this energy flux at the distance of the earth is about 1400 W m on an area normal to a beam of solar radiation. This value is called the solar constant. Due to the eccentricity of the earth s orbit as it revolves around the sun once a year, the earth is closer to the sun in January (perihelion) than in July (aphelion). This results in about a 7% difference in radiant flux at the outer limits of the atmosphere between these two times. 

Using Wien s displacement law, determine the mean effective temperature of the earth-atmosphere system if the resulting longwave radiation peaks at 11 /rm. Contrast the magnitude of the radiant flux at 11 pm with that at 50 pm. 

When these are derived with respect to the wavelength, and the wavelength value, whth the maximum value of radiation intensity, is solved for, the tesuh is Wien s law ... 

According to Wien s law, the wavelength representing the maximum point decreases with increasing temperature (Fig. 4.29). 

W. Wien (Wurzburg) the laws governing the radiation of heat. 

SOLUTION We can use Wien s law in the form T = constant/ max to determine the surface temperature of stars treated as hot black bodies ... 

The temperature of molten iron can be estimated by using Wien s law. If the melting point of iron is 1540°C, what will be the wavelength (in nanometers) corresponding to maximum intensity when a piece of iron melts ... 

Wien s law The wavelength corresponding to the maximum in the radiation emitted by a heated black body is inversely proportional to the absolute temperature. 

Wien s Displacement Law is proved by thermodynamic considerations and by experiment in contradistinction to Wien s Radiation Formula, which is only proved experimentally for small values of X. 

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