Wien s displacement law

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... 

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) ... 

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. 

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. 

Light emitted from a black body solely as a result of high temperature as in electric bulb is known as incandescence or thermal radiation. The quality and quantity of thermal radiation is a function of temperature only. The wavelength of most strongly emitted radiation in the continuous spectrum from black body is given by Wien s Displacement Law-, Amax T —h. (where h is Wien s constant = 2.898 X 10 3 m deg). 

The sun s total radiation output is approximately equivalent to that of a blackbody at 10,350°R (5750 K). However, its maximum intensity occurs at a wavelength that corresponds to a temperature of 11,070°R (6150 K) as given hy Wien s displacement law. A figure plotting solar irradiance versus spectral distribution of solar energy is given in Fig. 9. See also Solar Energy. 

The wavelength of radiation emitted with maximum power from a black body at temperature T is given by Wien s displacement law ... 

The theorem of the equipartition of energy when extended to the thermal equilibrium between matter and ether was very well confirmed as far as the infrared part of black-body radiation was concerned. Its extension to the ultraviolet domain, however, leads to absurd results, so that, at least for the time being, one is unable to derive the Boltzmann-Stefan law and Wien s displacement law without reference to thermodynamical results. At the present time one cannot see how these difficulties can be solved.217... 

A plot of EbA as a function of temperature and wavelength is given in Fig. 8-5a. Notice that the peak of the curve is shifted to the shorter wavelengths for the higher temperatures. These maximum points in the radiation curves are related by Wien s displacement law,... 

It is quite apparent from Fig. 8-63 that solar radiation which arrives at the surface of the earth does not behave like the radiation from an ideal gray body, while outside the atmosphere the distribution of energy follows more of an ideal pattern. To determine an equivalent blackbody temperature for the solar radiation, we might employ the wavelength at which the maximum in the spectrum occurs (about 0.5 /im, according to Fig. 8-63) and Wien s displacement law [Eq. (8-13)]. This estimate gives... 

If we know the surface temperature of a blackbody, we can predict the wavelength for maximal radiation from it. To derive such an expression, we differentiate Planck s radiation distribution formula with respect to wavelength and set the derivative equal to zero.4 The relation obtained is known as Wien s displacement law ... 

Besides the absorption of the various components of solar irradiation, additional infrared (IR), or thermal, radiation is also absorbed by a leaf (see Eq. 7.2 and Fig. 7-1). Any object with a temperature above 0 K ( absolute zero ) emits such thermal radiation, including a leaf s surroundings as well as the sky (see Fig. 6-11). The peak in the spectral distribution of thermal radiation can be described by Wien s displacement law, which states that the wavelength for maximum emission of energy, A,max, times the surface temperature of the emitting body, T, equals 2.90 x 106 nm K (Eq. 4.4b). Because the temperature of the surroundings is generally near 290 K, A,max for radiation from them is close to... 

We start this chapter with a discussion of eiectromaguetir. waves and the electromagnetic spectniiii, with particular emphasis on thermal radiation. Then we introduce the idealized blackhody, blackbody radiation, and black-body radiation ftinciion, together with the Sle/ati-Bolizniariii law, Planck s law, and Wien s displacement law. 

As the temperature increases, the peak of the curve in Fig. 12-9 shifts toward shorter wavelengths, TTie fvavelength at which the peak occurs for a specified temperature is given by Wien s displacement law as... 

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