Monochromatic emissive power

The first and second Planck-law constants c and C9 are respectively (3.740)(10- ) (Jm )/s and (1.4388)(10- ) m K. The term clearly a function only of the product XT, is given in Fig. 5-11 which may be visualized as the monochromatic emissive power versus wavelength measured in vacuo of a black surface at 1 K discharging in vacuo. 

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 ... 

In general, the emissivity of a solid is affected by the temperature as well as the wavelength of the radiation. The concept of monochromatic emissivity is related to the radiant emission by a solid at a specific wavelength. The monochromatic emissivity e is defined as the ratio of the monochromatic-emissive power of a solid Ex to the monochromatic-emissive power of a blackbody EbX at the same temperature and wavelength, i.e.,... 

Moreover, a solid is termed a gray body if its monochromatic emissivity ex is independent of the wavelength. The monochromatic-emissive power of a blackbody at a specific temperature and wavelength is given by Planck s formula... 

Ek Monochromatic-emissive power of radiation P p Partial pressure of the adsorbate Dimensionless pressure of... 

Ebk Monochromatic-emissive power of blackbody radiation Po adsorbate Saturated vapor pressure... 

X Parameter, defined by Eq. (1.14) Greek Symbols Xm Wavelength at which the monochromatic-emissive power of a blackbody is maximum... 

The hemispherical emissive power E is defined as the radiant flux density (W/m2) associated with emission from an element of surface area dA into a surrounding unit hemisphere whose base is copla-nar with dA. If the monochromatic intensity ( 2, X) of emission from the surface is isotropic (independent of the angle of emission, 2), Eq. (5-101) may be integrated over the 2k sr of the surrounding unit hemisphere to yield the simple relation Ex = nix, where >, = Ex(X) is defined as the monochromatic or spectral hemispherical 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)... 

FIG. 5-9 Spectral dependence of monochromatic blackbody hemispherical emissive power. 

As we learned with Fig. 8.2, nature provides radiation over a wavelength spectrum. The energy of monochromatic radiation is the monochromatic emissive power Ex, which we consider next. 

By definition, the relation between the monochromatic emissive power and the emissive power is... 

Figure 8.6 Black-body monochromatic emissive power.

Reconsider Ex. 8.3. For these radiation sources we wish to determine (a) the maximum monochromatic black-body emissive power and (b) the wavelength corresponding to the maximum emissive power,... 

Now, consider an enclosure filled with monochromatic radiation Ga, and place a monochromatically opaque (r =0) body into this enclosure (Fig. 8.12). Let the monochromatic reflectivity and emissive power of the body be pi and Fa, respectively. Under equilibrium, the first law of thermodynamics for the system enclosing the body gives... 

At a given temperature, if the ratio of the monochromatic emissive power of a surface to the monochromatic emissive power of the black body at the same wavelength remains constant over the entire wavelength spectrum,... 

The monochromatic emissive power in terms of frequency proves convenient for spectral integrations as well as for gas radiation (to be introduced in Chapter 10). 

The monochromatic emissive power of a blackbody Fs(l)(Wm 2m l) is related to temperature and wavelength by... 

---