Spectrum blackbody

We can sample the energy density of radiation p(v, T) within a chamber at a fixed temperature T (essentially an oven or furnace) by opening a tiny transparent window in the chamber wall so as to let a little radiation out. The amount of radiation sampled must be very small so as not to disturb the equilibrium condition inside the chamber. When this is done at many different frequencies v, the blackbody spectrum is obtained. When the temperature is changed, the area under the spechal curve is greater or smaller and the curve is displaced on the frequency axis but its shape remains essentially the same. The chamber is called a blackbody because, from the point of view of an observer within the chamber, radiation lost through the aperture to the universe is perfectly absorbed the probability of a photon finding its way from the universe back through the aperture into the chamber is zero. 

Figure 1-1 The Blackbody Radiation Spectrum. The short curve on the left is a Rayleigh function of frequency.

For simplicity, n should be as low as is consistent with small error. The retention of but two terms is feasible when one considers that if Otci is so fitted that the first absorption and the second following surface reflec tion are correct, then further attenuation of the beam by successive surface reflections makes the errors in those absorptions decrease in importance. Let the gas be modeled as the sum of one gray gas plus a clear gas, with the gray gas occupying the energy frac tion a of the blackbody spectrum and the clear gas the frac tion (1 — ). Then... 

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... 

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. 

Total heat transfer consists of radiation at different frequencies. The distribution of radiation energy in a spectrum and its dependency on temperature is determined from Planck s law of radiation. M ,and are the spectral radiation intensities for a blackbody ... 

When Planck used this relationship to calculate the spectrum of blackbody radiation, he came up with a result that agreed perfectly with experiment. More importantly, he had discovered quantum mechanics. Energy emitted by a blackbody is not continuous. Instead, it comes in tiny, irreducible packets or quanta (a word coined by Planck himself) that are proportional to the frequency of the oscillator that generated the radiation. 

Figure 5. Model spectra of a naked neutron star. The emitted spectrum with electron-phonon damping accounted for and Tsurf = 106 K. Left panel uniform surface temperature right panel meridional temperature variation. The dashed line is the blackbody at Tsurf and the dash-dotted line the blackbody which best-fits the calculated spectrum in the 0.1-2 keV range. The two models shown in each panel are computed for a dipole field Bp = 5 x 1013 G (upper solid curve) and Bp = 3 x 1013 G (lower solid curve). The spectra are at the star surface and no red-shift correction has been applied. From Turolla, Zane and Drake (2004).

Figure 22. Schematic overlay of the most intense IR absorptions for neutral acetone and acetone-dg with a 300-K blackbody emission spectrum. The intensity axis refers to the blackbody radiation only.

At low pressure, the only interactions of the ion with its surroundings are through the exchange of photons with the surrounding walls. This is described by the three processes of absorption, induced emission, and spontaneous emission (whose rates are related by the Einstein coefficient equations). In the circumstances of interest here, the radiation illuminating the ions is the blackbody spectrum at the temperature of the surrounding walls, whose intensity and spectral distribution are given by the Planck blackbody formula. At ordinary temperatures, this is almost entirely infrared radiation, and near room temperature the most intense radiation is near 1000 cm". ... 

Rising above the background emission, assumed to be that of a blackbody at 3000°K, is a broad 9.7-jam feature for the oxygen star. Between about 15 and 20 jim a much weaker excess emission feature is also evident. A measured absorption spectrum of amorphous olivine smoke particles (Kratschmer and Huffman, 1979) is shown for comparison. 

It is sometimes not necessary to know the absolute value of zm but rather the order of magnitude of ratio nm/zm, which might be called the occupancy ratio of the degrees of freedom by photons. This may be estimated as follows. Suppose that we knew that the spectrum was like that of a blackbody at temperature T. We could then use the well-known relation for the average number of photons per mode (degree of freedom),... 

Spectroscopy was to prove indispensable in unlocking the structure of atoms, particulary their electronic stmcture— but those developments would depend on other, later researchers. Max Planck s analysis of blackbody radiation and Bohr s theory of the hydrogen spectrum are just two examples. 

One of the problems which must be solved for quantitative measurements by emission is the need for a blackbody source at the temperature of measurement. And a variety of blackbody references have been used including a V-shaped cavity of graphite 164), a metal plate covered with a flat black paint1S6 160) and a cone of black paper l53). However, none of these methods of producing a blackbody reference spectrum are adequate. In most cases the efficiency of the reference has not been established. The most recent recommendation 1S0) is an aluminium cup painted with an Epley-Parsons solar black lacquer which has an emittance of greater than 98% over the infrared spectral range. 

The blackbody emission spectrum at right changes with temperature, as shown in the graph. Near 300 K, maximum emission occurs at infrared wavelengths. The outer region of the sun behaves like a blackbody with a temperature near 5 800 K, emitting mainly visible light. 

Infrared radiation in the range 4 000 to 200 cm-1 is commonly obtained from a silicon carbide globar, heated to near 1 500 K by an electric current. The globar emits radiation with approximately the same spectrum as a blackbody at 1 000 K (Box 20-1). 

Figure 3. A composite spectrum of SN 1987a observed on March 1 (Danziger et al. 1987) is compared with one of our best-fitting (absorbed) computed spectra, corresponding to the parameters indicated. Both the theoretical spectrum (triangles) and that of an (unabsorbed) blackbody at the same effective temperature have been displaced by the same amount for clarity (see separate scales). No theoretical points are shown at wavelengths shorter than that at which the other stars dominate the flux.

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