Wien’s law

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... 

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. 

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). 

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. 

Turning now to the wavelength distribution of the starlight. The emission from a black body must, by definition, produce radiation at all wavelengths, i.e. a wavelength distribution. It turns out for a black body that the wavelength at which the maximum radiation flux occurs is characteristic of the temperature and is given by Wien s Law ... 

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 ... 

Wien s law offers a simple relationship between the wavelength maximum k(max) and the thermodynamic temperature T ... 

Figure 9.23 Wien s law and black-body radiation as the temperature T of the black body is raised, so the wavelength maximum of the emitted radiation decreases. The area under the curve indicates the intensity of the energy emitted by the black body, and is proportional to 7 4...

The star in the numerical model has an inside and an outside. The outside is defined as the limit beyond which it becomes transparent. This boundary is called the photosphere, or sphere of light, for it is here that the light that comes to us is finally emitted. It is thus the visible surface of the star, located at a certain distance R from the centre, which defines the radius and hence the size of the star. The photosphere has a certain temperature with which it is a simple matter to associate a colour, since to the first approximation it radiates as a blackbody, or perfect radiator. Indeed, the emissions from such a body depend only on its temperature. The correspondence between temperature and colour is simple. In fact, the relation between temperature and predominant wavelength (which itself codifies colour) is given by Wien s law, viz. 

The cause of global warming from man-made atmospheric gases also stems from the same factor of atmospheric persistence, as well as their ability to absorb infrared light radiating from Earth to space. Thermal radiation from a radiant body has a distribution of wavelengths, with the maximum value given by Wien s law ... 

Wien s Law law that states the wavelength of maximum energy radiation from an object is inversely proportional to the surface temperature of the object Work product of force times displacement... 

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... 

Wien s law can be used to determine the temperature of stars, which can be treated as hot black bodies. For example, the maximum intensity of solar radiation occurs at 490 nm, so the surface temperature of the Sun must be about... 

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