Blackbody emissive power

An additional surface arrangement of importance is a single-zone surface enclosing gas. With the gas assumed gray, the simplest derivation of GSi is to note that the emission from surface Ai per unit of its blackbody emissive power is Ai i, of which the fractions g and (1 - G)ei are absorbed Dy the gas and the surface, respectively, and the surface-reflected residue always repeats this distribution. Therefore,... 

Fig. 8-5 (a) Blackbody emissive power as a function of wavelength and temperature, (b) comparison of emissive power of ideal blackbodies and gray bodies with that of a real surface. 

With no windows at all, the heat transfer would have been the difference in blackbody emissive powers,... 

Blackbody Radiation Engineering calculations involving thermal radiation normally employ the hemispherical blackbody emissive power as the thermal driving force analogous to temperature in the cases of conduction and convection. A blackbody is a theoretical idealization for a perfect theoretical radiator i.e., it absorbs all incident radiation without reflection and emits isotropically. In practice, soot-covered surfaces sometimes approximate blackbody behavior. Let /.V, = /. A... 

Integration of Eq. (5-102) over all wavelengths yields the Stefan-Boltzman law for tne hemispherical blackbody emissive power... 

Heat capacity per unit mass, J kg 1-K 1 Shorthand notation for direct exchange area Area of enclosure or zone t, m2 Speed of light in vacuum, m/s Planck s first and second constants, W-m2 and m-K Particle diameter and radius, Jim Monochromatic, blackbody emissive power, W/(m2 lm)... 

Exponential integral of order n, where n = 1, 2,3,.. . Hemispherical emissive power, W/m2 Hemispherical blackbody emissive power, W/m2 Volumetric fraction of soot Blackbody fractional energy distribution Direct view factor from surface zone i to surface zonej Refractory augmented black view factor F-bar Total view factor from surface zone i to surface zonej Planck s constant, J s Heat-transfer coefficient, W/(m2 K)... 

Conversion of gray-gas total exchange areas GS and SS to their nongray form depends on the fact that the relation between radiative transfer and blackbody emissive power dT is linear and proportional. The gray-gas-equivalent emissivity is applicable only to the... 

B Understand the idealized blackbody, and calculate the lolal and spectral blackbody emissive power,... 

The Stefan-Boltzmann law in Eq. 12-3 gives the total blackbody emissive power f. i, which is the sum of the radiation emitted over all wavelengths. Sometimes we need to know the spectral blackbody emissive power, which is the amount of radiation energy emitted by a blackbody at a thermodynamic temperature T per unit time, per unit surface area, and per unit wavelength about the wavelength X. For example, we are more interested in the amount of radiation an incandescent lighthulb emits in the visible wavelength spectrum than we are in the total amount emitted. 

The retalion for the spectral blackbody emissive power was developed by Max Planck in 1901 in conjunction with his famous quantum theory. This relation is known as Planck s law and is expressed as... 

The variation of the spectral blackbody emissive power with wavelength is plotted in Fig. 12-9 for selected temperatures. Several observations can be made from this figure ... 

FIGURE 12-9 Tlie variation of the blackbody emissive power with wavelength for several temperatures. 

It is left as an exercise to show that integration of the spectral blackbody emissive power over the entire wavelength spectrmn gives the total blackbody emissive power E ... 

Consider a 20-cm-dlameter spherical ball at 800 K suspended in air as shown in Fig. 12-12. Assuming the ball closely approximates a blackbody, determine a) the total blackbody emissive power, (h) the total amount of radiation emitted by the ball in 5 min, and (c) the spectral blackbody emissive power at a wavelength of. 3 (im. 

SOLUTION An isothermal sphere is suspended in air. The total blackbody emissive power, the total radiation emitted in 5 min, and the spectral blackbody emissive power at 3 p.m are to be determined. 

Analysis (a) The tolal blackbody emissive power is determined from the Stefan-Boltzmann law to be... 

C Define the total and spectral blackbody emissive powers. How are they related to each other How do they differ ... 

EI = [E,8, ] = [an8,] Diagonal matrix of surface blackbody emissive powers. 

Each surface emits radiation based on its temperature. The ideal radiator is called a blackbody. The rate of energy emission per unit area, tf, is also termed blackbody emissive power, E, and is given by the Stefan-Boltzmann law. 

Radiative intensity is related to the blackbody emissive power. To illustrate, consider an isotropic system where the intensity is independent of angle. The total energy flux at dA throughout the hemisphere of 2ir steradians is an integration of Equation 4.49. It must also be the total emissive power of the element. Therefore,... 

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