Kirchhoff *s law

Thermal Emission Laws. AH bodies emit infrared radiation by virtue of their temperature. The total amount of radiation is governed by Kirchhoff s law, which states that a body at thermal equiUbrium, ie, at the same temperature as its surroundings, must emit as much radiation as it absorbs at each wavelength. An absolutely blackbody, one that absorbs all radiation striking it, must therefore emit the most radiation possible for a body at a given temperature. The emission of this so-called blackbody is used as the standard against which all emission measurements are compared. The total radiant emittance, M., for a blackbody at temperature Tis given by the Stefan-Boltzmaim law,... 

The emissivity, S, is the ratio of the radiant emittance of a body to that of a blackbody at the same temperature. Kirchhoff s law requires that a = e for aH bodies at thermal equHibrium. For a blackbody, a = e = 1. Near room temperature, most clean metals have emissivities below 0.1, and most nonmetals have emissivities above 0.9. This description is of the spectraHy integrated (or total) absorptivity, reflectivity, transmissivity, and emissivity. These terms can also be defined as spectral properties, functions of wavelength or wavenumber, and the relations hold for the spectral properties as weH (71,74—76). 

Figure 15.23 KIrchhoff s law - sum of currents entering a node is zero...

Equations (24-3) and (24-4) correspond to Kirchhoff s laws for electrical networks. Figure (24-2) gives the voltage distribution for every point in space for a given field strength. 

In comparing the radiative properties of materials to those of a blackbody, fhe terms absorptivity and emissivity are used. Absorptivity is the amount of radiant energy absorbed as a fraction of the total amount that falls on the object. Absorptivity depends on both frequency and temperature for a blackbody if is 1. Emissivity is the ratio of the energy emitted by an object to that of a blackbody at the same temperature. It depends on both the properties of fhe subsfance and the frequency. Kirchhoff s law states that for any substance, its emissivity at a given wavelength and temperature equals its absorptivity. Note that the absorptivity and emissivity of a given substance may be quite variable for different frequencies. 

Kirchhoff s law The relationship that exists between the absorptivity and emissiv-ity of radiating bodies. It is the capacity of a body to absorb radiation, w hich varies with the wavelength of the incident radiation and the angle of incidence. 

Usually the electrical resistance of a separator is quoted in relation to area in the above case it is 57 mil cm2. In order to quote it for other areas, due to the parallel connection of individual separator areas, Kirchhoff s law has to be taken into account ... 

The temperature variation of the standard reaction enthalpy is given by Kirchhoff s law, Eq. 23, in terms of the difference in molar heat capacities at constant pressure between the products and the reactants. 

Derive Kirchhoff s law for a reaction of the form A + 2 B — 3 C + D by considering the change in molar enthalpy of each substance when the temperature is increased from T, to T2. 

Kirchhoff s law The relation between the standard reaction enthalpies at two temperatures in terms of the temperature difference and the difference in heat capacities (at constant pressure) of the products and reactants. 

William Prout s composite atoms hypothesis. G. Kirchhoff and R. Bunsen discover spectral analysis and significance of Fraunhofer lines Kirchhoff s law. 

The temperature dependence of the standard enthalpy is related by Kirchhoff s law ... 

Equation (4.87) was obtained under the assumption of strict thermodynamic equilibrium between the particle and the surrounding radiation field that is, the particle at temperature T is embedded in a radiation field characterized by the same temperature. However, we are almost invariably interested in applying (4.87) to particles that are not in thermodynamic equilibrium with the surrounding radiation. For example, if the only mechanisms for energy transfer are radiative, then a particle illuminated by the sun or another star will come to constant temperature when emission balances absorption but the particle s steady temperature will not, in general, be the same as that of the star. The validity of Kirchhoff s law for a body in a nonequilibrium environment has been the subject of some controversy. However, from the review by Baltes (1976) and the papers cited therein, it appears that questions about the validity of Kirchhoff s law are merely the result of different definitions of emission and absorption, and we are justified in using (4.87) for particles under arbitrary illumination. 

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. 

The classical emission profile, Eq. 5.72, may be converted to an absorption profile with the help of Kirchhoff s law, Eq. 2.70, which relates the absorption coefficient a to the emitted power per unit frequency interval per unit volume, with the help of Planck s law, Eq. 2.71, according to... 

This relation is called Kirchhoff s law. To use it, we need to know ACP, the difference between the molar constant-pressure heat capacities of the products and reactants ... 

STRATEGY To use Kirchhoff s law, we need to know the molar heat capacities of the reactants and products these can be found in Appendix 2A. Combine them in the same way that enthalpies of formation would be combined to calculate a reaction enthalpy and then substitute in Eq. 32. Note that the temperatures must be expressed in kelvins. 

In emission spectrometry, the sample is the infrared source. Materials emit infrared radiation by virtue of their temperature. KirchhofF s law states that the amounts of infrared radiation emitted and absorbed by a body in thermal equilibrium must be equal at each wavelength. A blackbody, which is a body having infinite absorptivity, must therefore produce a smooth emission spectrum that has the maximum possible emission intensity of any body at the same temperature. The emissivity, 8, of a sample is the ratio of its emission to that of a blackbody at the same temperature. Infrared-opaque bodies have the same emissivity at all wavelengths so they emit smooth, blackbody-like spectra. On the other hand, any sample dilute or thin enough for transmission spectrometry produces a structured emission spectrum that is analogous to its transmission spectrum because the emissivity is proportional to the absorptivity at each wavelength. The emissivity is calculated from the sample emission spectrum, E, by the relation... 

Since the background of infrared emission spectroscopy is not so well established as for absorption spectroscopy, it is more difficult to predict the intensity of infrared emission bands. However, simplified calculations involving Planck s radiation law and Kirchhoff s law (68), and Einstein s emission and absorption coefficients (64), show that an emission band... 

By applying the second Kirchhoff s law to the equivalent electrical circuit of the ED stack (Figure 9), the overall potential drop across an ED stack can be written as ... 

Finally, we should mention Kirchhoff s law. The emissivity e expresses which fraction a body of temperature T emits to bodies of lower temperature. If e = 1, we speak of black-body radiation, otherwise of gray-body radiation. Kirchhoff s law compares the emissivity a with the absorptivity a of a body when exposed to incident radiation from a body with a higher temperature and states that... 

This equation is known as Kirchhoff s law in integral form. It enables us to calculate the heat of reaction at different temperatures by knowing die heat of reaction at one temperature, say, 298K, and heat capacities of reactants and products. 

If external potentials are applied to a system of several interconnected channels, the respective field strength in each channel will be determined by Kirchhoff s laws in analogy to an electrical network of resistors [28]. Ideally, electrokinetically driven mass transport in each of the channels will take place according to magnitude and direction of these fields. This allows for complex fluid manipulation operations in the femtoliter to nanoliter range without the need of any active control elements, such as external pumps or valves. This is of particular relevance due to the demanding limitations with respect to void volumes in the system (see Sect. 2). 

It is instructive to explicitly consider the charging process of eqc. Eq. (63) by a constant current I (Figure 38). According to Kirchhoff s laws, the voltage response is given by ... 

According to the superposition theorem of system theory for linear responses, this response to a step-function in the current can be employed to deduce the impedance behavior. As regards a qualitative discussion, one can adopt the above description by just replacing short/long times by high/small frequencies. Quantitatively the impedance is given by a Laplace transformation of Eq. (64) (or equivalently by applying Kirchhoff s laws to the equivalent circuit (Eq. (63))) with the result... 

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