Rate of energy absorption

Since the absorption spectrum is a ratio it is amenable to other interpretations. One such interpretation is that the absorption spectrum is the ratio of energy absorbed to energy incident. From this perspective, the quantity /)co(d/d0< li 0l f 0) is interpreted as the rate of energy absorption (per unit volume), since d E/d t = /)co(d AVd t) while tire quantity E dha is interpreted as the incident energy flux, which depends only on the field intensity and is independent of frequency. 

We now proceed to the spectrum, or frequency-dependent response [44, 42]. The power, or rate of energy absorption, is given by... 

Note the presence of the ra prefactor in the absorption spectrum, as in equation (Al.6.87) again its origm is essentially the faster rate of the change of the phase of higher frequency light, which in turn is related to a higher rate of energy absorption. The equivalence between the other factors in equation (Al.6.110) and equation (Al.6.87) under linear response will now be established. 

A. State-to-State Rate of Energy Absorption or Emission... 

Many common polymers, polymeric additives and lubricants oxidise so rapidly after impact in liquid oxygen that they are hazardous. Of those tested, only acrylonitrile-butadiene, poly(cyanoethylsiloxane), poly(dimethylsiloxane) and polystyrene exploded after impact of 6.8-95 J intensity (5-70 ft.lbf). All plasticisers (except dibutyl sebacate) and antioxidants examined were very reactive. A theoretical treatment of rates of energy absorption and transfer is included [1], Previously, many resins and lubricants had been examined similarly, and 35 were found acceptable in liquid oxygen systems [2],... 

The transition probability P is proportional to the square of the microwave power level. Equation (26) shows that if the product of the microwave power level and the relaxation time are sufficiently small so that 2PT 1, the rate of energy absorption in the sample (signal amplitude) will be proportional to the population difference and to the power level. If 2PTi 5>> 1, saturation occurs and the rate of energy absorption will no longer be proportional to the microwave power level. 

Since the rate of energy absorption is proportional to An0, it is perhaps worthwhile to examine this population difference at equilibrium. According to the Boltzmann law... 

Here p is dipole operator and E(t) is electric field in optical radiation. Due to the application of V(t), the system becomes nonstationary and the rate of energy absorption can be calculated ... 

That is, the rate of energy absorption Q is linearly related to the imaginary part of linear susceptibility x( >). 

The main difference between photochemical and thermal reaction is the presence of a radiation-activated step. The rate of reaction of this step is proportional to the local volumetric rate of energy absorption (LVREA). For any emission model, the LVREA is a function of the spatial variables, of the physical properties and geometrical characteristics of the lamp-reactor system, and some physicochemical properties of the reacting mixture. The most important design parameter that is pertinent in photochemical and photocatalytic reactions is the effective attenuation coefficient. 

Alfano, O.M., Romero, R.L., and Cassano, A.E. A cylindrical photoreactor irradiated from the bottom. 111. Measurement of absolute values of the local volumetric rate of energy absorption. Experiments with polychromatic radiation . Chem. Eng. Sci. 41,1163 (1986). 

The exchange of radiation is based upon two laws. The first, known as Kirchoff s law, states that the ratio of the emissive power to the absorptivity is same for all bodies in thermal equilibrium. The emissive power of a body, E, is the radiant energy emitted from unit area in unit time. A body of area Ai and emissivity E, therefore, emits energy at a rate E A. If the radiation falling on unit area of the body is E, the rate of energy absorption is E, aiAi, where ui is the absorptivity. At thermal equilibrium, E aiAx. For another body in the same environment, E a Aj = EjAj, leading to Eq. (36)... 

Consider irradiation of pure acrylonitrile (density = 0.81 g/cm ) at 20°C with 7-rays, with a dose rate of 10 rads/h. Calculate (a) the rate of energy absorption and (b) the rate of initiating radical formation per unit volume of the monomer. (100-eV yield of initiating radicals = 5.0)... 

The exposure to radiation is the product of the absorbed dose rate, which is a rate of energy absorption, and the exposure Ume. Most of the injuries listed above are of the threshold type. The dosage received must exceed a minimum before any physiological effect is observed. Above this level, small dose rates for a long period of exposure time are less injurious than an equivalent total dosage comprised of a very-high-level dose rate for a much smaller period of time. From an engineering viewpoint, the dose rate must be expressed in quantitative units as discussed next. 

Consider Ax = l/p for a unit gram mass of material with an exposed frontal plane area of 1 cm , where p is the density of the absorbing substance in grams per cubic centimeter. Since E is the energy in millions of electron volts (Mev) per particle or photon of radiation, then the rate of energy absorption or dose rate is... 

By definition, the instantaneous rate of energy absorption per unit volume, EA, is given by the product of the shear stress a and the shear rate y (23) ... 

Figure 6 Mixing energy versus rate of energy absorption of gum natural rubber samples...

---