Perfect absorber

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. 

Here ko = 471 gD is the rate constant for a diffusion-controlled reaction (Smoluchowski rate constant) for a perfectly absorbing sphere. For long times, kf t) approaches its asymptotic constant value kf = kofkD/(kqf + kD) as... 

Fluid motion acts to decrease the diffusion boundary layer thickness. Strategies of the microorganism to increase solute flux by decreasing its size or surface concentrations of the solute, c°, will be examined in Section 6. In this section, the solute concentration at the surface of the organism, c°, is assumed to be zero, i.e. the cell is a perfect absorber (sink), since this will provide an upper limit for the importance of fluid motion. It is clear that if fluid motion has no effect for a perfect absorber, it will have no effect for an imperfect one. 

The temperature of exposed samples is dependent on both the air temperature in the cabinet and the absorbance of direct radiation. Temperature is usually measured with a black panel thermometer, which gives the surface temperature of a perfectly absorbing material. White panel thermometers are also commonly used which measure the other extreme. The actual temperature reached by a test piece depends on the material and its colour. It will also depend on the air temperature and velocity so that both the air and black panel temperatures should be controlled. ISO 11403-3 [23] defines three sets of conditions in air with the black standard temperature at 65 °C (ISO 4892-2 Method A [27]), behind glass at the same temperature (ISO 4892-2 Method B [27]), and behind glass at 100 °C. 

If the earth is a perfect absorber, the concentration of material at the surface is zero. The form of the vertical distribution can be obtained by the method of an image source, with the change that we now subtract the distribution from the source at -z from that for the source at +z. The resulting vertical distribution is... 

Atoms and molecules absorb only specific frequencies of radiation dictated by their electronic configurations. Under suitable conditions they also emit some of these frequencies. A perfect absorber is defined as one which absorbs all the radiation falling on it and, under steady state conditions, emits all frequencies with unit efficiency. Such an absorber is called a black body. When a system is in thermal equilibrium with its environment rates of absorption and emission are equal (Kirchhoff s law). This equilibrium is disturbed if energy from another source flows in. Molecules electronically excited by light are not in thermal equilibrium with their neighbours. 

A. Scrinzi, Infinite-range exterior complex scaling as a perfect absorber in time-dependent problems, Phys. Rev. A 81 (5) (2010) 053845. 

The absorptivity, a, is the ratio of the absorbed energy to the incident energy from the source. A perfect absorber is called a black body. Nonperfect absorbers, 1 > a > 0, are known as grey bodies. 

The emissivity, s, is the ratio of the emitted energy to that of a perfect emitter. A perfect emitter is also a perfect absorber, a black body. For grey bodies, e = a = constant is often assumed. Values of s for many materials are given in the literature, e.g. ref. 7. 

It follows from Eq. (10.15) that a slowly varying continuum acts as an irreversible perfect absorber since in this approximation bx(t) decreases monotoni-cally (though not necessarily as a simple exponential) with time. 

A blackbody absorbs the entire radiation incident on it. Tljat is, a blackbody is a perfect absorber (a = 1) as it is a perfect emitter. 

The same approach can be used for instantaneous reactions by putting ik - abs refi whcrc is the probability density for a perfectly absorbing reactive surface [63]. 

Brouard. S., Macias, D. and hluga, J.G. (1994) Perfect absorbers for stationary and wavcpackct scattering, J. Phys. A 27, L439-L445. 

Perfect absorber and emitter of radiation -> Intensity of radiation for a series of temperatures... 

It is most important that the shape of the target allows it to act as a perfect absorber. Almost always some additional systems are required in the chamber to absorb the sound wave and thereby avoid side influences from reflected or standing waves on the target. Typically paraffin wax or linen are used for this purpose. 

A concept closely related to emissive power is emissivity, which describes how black the surface is. Recall that a blackbody is a perfect absorber it is also a perfect emitter. By comparing with a blackbody, a unique datum can be defined. The emissivity of a surface is the ratio of its emissive power to the emissive power of the blackbody at the same temperature ... 

The concept of hlackhody is determining the basis for describing the radiation properties of real surfaces. The black body denotes an ideal radiative surface which absorb all incident radiation, being a diffuse emitter and emit a maximum amount of energy as thermal radiation for a given wavelength and temperature. The black body can be considered as a perfect absorber and emitter. 

The simplest treatment of diffusive encounters considers two noninteracting hard spheres that have radii r, and r2, diffusion constants D and Di, and isotropic reactivities such that any collision (i.e., when the distance between the two spheres is equal to the sum of their radii) leads to the reaction. This model requires solution of the Smoluchowski equation215 with a perfectly absorbing condition at R = r, + r2. The resulting rate constant k(R) has the simple form... 

FIGURE 7.4 Blackbody characteristics for isothermal enclosures (a) intensity is the same in all directions, and irradiation on any surface inside the enclosure is equal to the blackbody emissive power, and (b) emission through a small aperture approximates that of a blackbody, and the cavity acts as a perfect absorber. 

M. Planck, Theorie der Warmestrahlung, Formula (64). The factor 2 in Planck s formula arises from his considering a perfectly reflecting element, while we have a perfectly absorbing one. 

A blackbody is one that is a perfect absorber of radiation it absorbs all the radiation falling on it, without reflecting any. More relevant for us, the radiation emitted by a hot blackbody depends (as far as the distribution of energy with wavelength goes) only on the temperature, not on the material the body is made of, and is thus amenable to relatively simple analysis. The sun is approximately a blackbody in the lab a good source of blackbody radiation is a furnace with blackened insides and a small aperture for the radiation to escape. In the second half of the nineteenth century the distribution of ... 

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