Spectral emissive power black body

If the emissive power E of a radiation source-that is the energy emitted per unit area per unit time-is expressed in terms of the radiation of a single wavelength X, then this is known as the monochromatic or spectral emissive power E, defined as that rate at which radiation of a particular wavelength X is emitted per unit surface area, per unit wavelength in all directions. For a black body at temperature T, the spectral emissive power of a wavelength X is given by Planck s Distribution Law ... 

The wavelength and temperature dependency given by (5.37) correspond to a relationship found by W. Wien [5.3] in 1896 to be approximately valid for the hemispherical spectral emissive power M S(X,T ) of an ideal radiator, a black body, with a temperature T. We will come back to the properties of black bodies in section 5.1.6 and more extensively in 5.2.2. In our example a spectral irradiance E M s has been assumed, so that its indirect dependence on T appears explicitly in (5.37). 

Hollow enclosure radiation and radiation of a black body (a x = 1) have identical properties. The black body radiates diffusely from (5.18) it holds for its hemispherical spectral emissive power that... 

A black body is defined as a body where all the incident radiation penetrates it and is completely absorbed within it. No radiation is reflected or allowed to pass through it. This holds for radiation of all wavelengths falling onto the body from all angles. In addition to this the black body is a diffuse radiator. Its spectral intensity LXs does not depend on direction, but is a universal function iAs(A,T) of the wavelength and the thermodynamic temperature. The hemispherical spectral emissive power MXs(X,T) is linked to Kirchhoff s function LXs(X,T) by the simple relationship... 

We refrain from deriving the equations for the spectral intensity and the hemispherical spectral emissive power of a black body, found by M. Planck [5.6], for... 

Fig. 5.23 Hemispherical spectral emissive power MXs(X,T) of a black body according to Planck s radiation law (5.50)...

Table 5.3 Hemispherical spectral emissive power of a black body divided by the fifth power of the temperature, according to (5.54) and fraction function F(0, AT) according to (5.60) as a function of the product AT...

Fig. 5.30 Hemispherical spectral emissive power M (A, T) of a real body compared to the hemispherical spectral emissive power M g(A, T) of a black body at the same temperature. The hatched area represents the emissive power M(T) of the real body 0...

A radiator emits its maximum hemispherical spectral emissive power at Amax = 2.07 /im. Estimate its temperature T and its emissive power M(T), under the assumption that it radiates like a black body. 

The oven wall is exposed to radiation from glowing coal the spectral irradiance E can be assumed to be proportional to the hemispherical spectral emissive power M s(Tk) of a black body at Tk = 2000 K. 

Although responsivity is also a valid figure of merit for detectors operating in the visible spectrum, the units are sometimes different. Since the lumen is a standard unit of visible radiant power, it is common practice to measure the responsivity of detectors such as photomultipliers in units of amps/lumen. Again, either a spectral or a black body reference can be employed. A useful black body reference temperature for visible detectors is 2870 K, the temperature at which the peak emission is at 1 pm. 

The total emission of radiant energy from a black body takes place at a rate expressed by the Stefan-Boltzmann (fourth-power) lav/ while its spectral energy distribution is described by Wien slaws, ormore accurately by Planck s equation, as well as by a n umber of oilier empirical laws and formulas, See also Thermal Radiation,... 

Consider a 20-cm X 20-cm X 20-cm cubical body at 750 K suspended in the air. Assuming the body closely approximates a blackbody, determine (a) the rate at which the cube emits radiation energy, in W and (h) the. spectral black-hody emissive power at a wavelength of 4 pm. 

Now there is a theorem of Kirchhoff s (1859) which states that the ratio of the emissive and absorptive powers of a body depends only on the temperature of the body, and not on its nature otherwise radiative equilibrium could not exist within a cavity containing substances of different kinds. (By emissive power is meant the radiant energy emitted by the body per unit time, by absorptive power the fraction which the body absorbs of the radiant energy which falls upon it.) By a black body is meant a body with absorptive power equal to unity, i.e. a body which absorbs the whole of the radiant energy falling upon it. The radiation emitted by such a body—called black radiation —is therefore a function of the temperature alone, and it is important to know the spectral distribution of the intensity of this radiation. The following pages are devoted to the determination of the law of this intensity. 

The solar luminosity (total radiant power emitted) is 3.861(T W, of which 1373 W/m reaches the top of the earth s atmosphere. To a zeroth approximation the sun can be considered a black body with an effective temperature of 5780 K, which implies a peak in the radiation at around 0.520 pm (5200 A). The actual solar spectral emission is more complex, especially at ultraviolet and shorter wavelengths. The graph below, which was taken from Reference 1, summarizes the solar irradiance at the top of the atmosphere in the range 0.3 to 10 pm. 

Figure 9.33. Spectral black-body emissive power...

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