Blackbody radiation, energy density

If we think in terms of the particulate nature of light (wave-particle duality), the number of particles of light or other electi omagnetic radiation (photons) in a unit of frequency space constitutes a number density. The blackbody radiation curve in Fig. 1-1, a plot of radiation energy density p on the vertical axis as a function of frequency v on the horizontal axis, is essentially a plot of the number densities of light particles in small intervals of frequency space. 

The unique feature in spontaneous Raman spectroscopy (SR) is that field 2 is not an incident field but (at room temperature and at optical frequencies) it is resonantly drawn into action from the zero-point field of the ubiquitous blackbody (bb) radiation. Its active frequency is spontaneously selected (from the infinite colours available in the blackbody) by the resonance with the Raman transition at co - 0I2 r material. The effective bb field mtensity may be obtained from its energy density per unit circular frequency, the... 

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. 

Variations in the temperature of a blackbody used as the source in a spectrometer. The energy density of blackbody radiation is given by the well-known formula ... 

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... 

The Arrhenius-like temperature dependence obtained, which however gives rise to unreasonable Irequency factors, can then be rationalized on the basis of the temperature dependence of the blackbody radiation. At higher temperatures, the energy density per unit wavelength of the blackbody radiation increases with the maximum in the distribution shifted to higher frequency. Also, at a given frequency the intensity of radiation emitted varies approximately as In / oc -T" Therefore, as the temperature increases, so too does the intensity of the radiation and with it the rate of energization of the cluster ion and, consequently, the rate of unimolecular dissociation. Thus the temperature dependence is entirely consistent with a radiative mechanism for dissociation. 

FIGURE 5.1 Energy density U(X) emitted as a function of wavelength for blackbodies at two different temperatures. The visible region (X ss 0.4-0.7/xm) is shaded near the center. The total power radiated per unit area rises dramatically as the temperature increases. The spectrum shifts to shorter wavelengths as well. 

According to Planck, blackbody radiation implies a universal dependence of the energy density per photon energy interval d(huj). This results in an energy current density djV,bb per photon energy interval d(fuj) given by... 

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. 

Fig. 4.8. Efficiency rj, open-circuit voltage Voc, and short-circuit current density jsc as a function of the band gap a of a 2-band system illuminated by blackbody radiation at 5 800 K with an incident energy current density of 1.39 kW/m2...

In 1901 Planck finally explained the frequency and temperature dependence of blackbody radiation, and ushered in the age of quantum physics, by introducing the quantization of the oscillators that Rayleigh had discussed. (Planck assumed that these oscillators were in the walls of the Hohlmum and that the radiation was in equilibrium with them.) The energy density (energy per unit volume) [m(v, T)/V] dv at the temperature i, in the frequency range between v and v + dv, is given by... 

We will express the IR emitted by a leaf at a temperature 74eaf using the Stefan-Boltzmann law (Eq. 6.18a), which describes the maximum rate of radiation emitted per unit area. For the general emission case we incorporate a coefficient known as the emissivity, or emittance (e)y which takes on its maximum value of 1 for a perfect, or blackbody, radiator. The actual radiant energy flux density equals (Tact )4 (Eq. 6-18b), which is the same as actual temperatures to describe... 

The energy density distribution of blackbody radiation as a function of wavelength. 

The average spectral energy density in a blackbody cavity radiator, ct) is given in eqn [1],... 

Fields in thermal equilibrium can be more generally referred to as thermal radiation. One of the characteristic properties of thermal radiation is that its energy density is only a function of temperature unlike the ideal gas, the number of particles of each kind itself depends on the temperature. Blackbody... 

For a thermal radiation source, for example the blackbody radiator of Sect. 2.2 with a spectral energy density p, the spectral radiance L (v) is independent of and can be expressed by... 

The amount of thermal radiation expected from a given planet depends in detail on the physical characteristics of the planet s atmosphere and surface. A starting point for understanding the observed flux densities of the planets is to assume that the planets are blackbodies in equilibrium with the energy they receive from the Sun and that which is radiated into free space. The radiation energy incident... 

Fig. 4.1. Energy current densities per photon energy of AMO (dotted line) and AM 1.5 (solid line, [1]) solar radiation. The thin solid line is the spectrum of a 5 800 K blackbody emitted into the solid angle 6.8 x 10-5...

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