Radiation from blackbodies

By using absorbing filters, the radiation from blackbody sources at higher temperatures can be down-rated to temperatures within the calibration range of the pyrometer. As a result, the range of the pyrometer can be extended well above the melting temperature of gold. 

An excellent and readable discnssion of all aspects of the interaction of light with matter, from blackbody radiation to lasers and nonlinear optics. 

The total energy radiating from a blackbody of unit area is given by the Stefan-Boltzman law ... 

Blackbody Radiation Engineering calculations of thermal radiation from surfaces are best keyed to the radiation characteristics of the blackbody, or ideal radiator. The characteristic properties of a blackbody are that it absorbs all the radiation incident on its surface and that the quality and intensity of the radiation it emits are completely determined by its temperature. The total radiative fliix throughout a hemisphere from a black surface of area A and absolute temperature T is given by the Stefan-Boltzmann law ... 

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) ... 

The radiation from a blackbody is conhnuous over the electromagnetic spectrum. The use of the term black in blackbody, which implies a particular color, is quite misleading, as a number of nonblack maferials approach blackbodies in behavior. The sun behaves almost like a blackbody snow radiates in the infrared nearly as a blackbody. At some wavelengths, water... 

This is Planck s famous radiation law, which predicts a spectral energy density, p , of the thermal radiation that is fully consistent with the experiments. Figure 2.1 shows the spectral distribution of the energy density p for two different temperatures. As deduced from Equation (2.2), the thermal radiation (also called blackbody radiation) from different bodies at a given temperature shows the same spectral shape. In expression (2.2), represents the energy per unit time per unit area per frequency interval emitted from a blackbody at temperature T. Upon integration over all frequencies, the total energy flux (in units of W m ) - that is, Atot = /o°° Pv Av - yields... 

Another consideration in flames is radiatioiL The light that one sees in a flame is mostly fluorescence from the radiation of particular radical species formed in electronically excited states. (The blue color from CH4 flames is CH emission.) Gases also radiate blackbody radiation, primarily in the infiared. The glow from burning wood or coal is blackbody emission radiated from the surface. 

Example 10-2 Everyone has poked a campfire at night and watched the sparks fly up. They glow a bright red, which indicates that they are emitting blackbody radiation from a source with a surface temperature of -1200°C. You have also noticed (if you were thinking about scientific matters at the time) that their color does not change until they suddenly disappear. The time for this reaction varies, but they seem to glow for a few SdC and then suddenly disappear. 

Clearly, 254 K is much colder than the typical temperatures around 288 K (15°C) found at the earth s surface. This difference between the calculated effective temperature and the true surface temperature is dramatically illustrated in Fig. 14.4, which shows the spectra of infrared radiation from earth measured from the Nimbus 4 satellite in three different locations, North Africa, Greenland, and Antarctica (Hanel et al., 1972). Also shown by the dotted lines are the calculated emissions from blackbodies at various temperatures. Over North Africa (Fig. 14.3a), in the window between 850 and 950 cm-1, where C02, O-, HzO, and other gases are not absorbing significantly, the temperature corresponds to blackbody emission at 320 K due to the infrared emissions from hot soil and vegetation. 

Calculate the power per unit area (the exitance, W/m2) radiating from a blackbody at 77 K (liquid nitrogen temperature) and at 298 K (room temperature). 

The system we now consider has a lower energy level at ex and an upper level at 2. The occupation of the states at these levels in equilibrium with the blackbody radiation from the surroundings (300 K) obeys Fermi statistics. 

The generation rate AG is calculated from (4.2) for a blackbody spectrum of 5 800 K incident from a solid angle 6.8 x 10—5, as subtended by the sun. As can be seen from Fig. 4.1, this blackbody spectrum is very close to the AMO spectrum and gives a total energy current density of 1.39 kW/m2, compared with 1.35 kW/m2 for AMO. The temperature of the solar cell and its surroundings is 300 K, which determines a reverse current of only 3x 10-16 A/m2 due to the absorption of blackbody radiation from the surroundings. 

Equation (11.29) is KirchhofPs law of radiation. The law states that the spectral emissivity for the emission of radiation at temperature T is equal to the spectral absorptivity for radiation from a blackbody at the same temperature T. The relation... 

We are frequently interested in the amount of energy radiated from a blackbody in a certain specified wavelength range. The fraction of the total energy radiated between 0 and A is given by... 

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... 

Fused quartz transmits 90 percent of the incident thermal radiation between 0.2 and 4 fim. Suppose a certain heat source is viewed through a quartz window. Vhat heat flux in watts will be transmitted through the material from blackbody radiation sources at (a) 800°C, (b) 550°C, (c) 250°C, and (d) 70°C ... 

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 ... 

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