Isothermal enclosure

The performance of the apparatus in the isothermal enclosure of the equilibrium diagram, Figure A. 1, which may be a fuel cell or an electrolyser depending on which way the equilibrium is tilted, is 1.23Vn, 237.1 AG. That equal and opposite performance could not be achieved by a PEFC with irreversible chemistry at its cathode as discussed below. 

For a single reversible process between two sets of fixed conditions, the work is independent of the reversible path. However, in a network of reversible processes, such as Figure A.l, alteration of the pressure and temperature of the isothermal enclosure alters the pressure ratio of, for example, the fuel isothermal expander. The power output of Figure A.l is therefore variable and not a constant, merely because it is reversible. The maximum power, the fuel chemical exergy, is obtained from an electrochemical reaction at standard temperature, Tq, and sum of reactant and product pressures, Pg, with isothermal expanders only and without a Carnot cycle. 

The fuel cells and reformer are in isothermal enclosure, at To, coupled to die environment. 

In other texts, the fuel chemical exergy is thought of as a value independent of temperature and pressure, like combustion enthalpy. Instead it has, above, a maximum at FgTg. The major difference in calculation routes is that the author uses equilibrium conditions dictated by the equilibrium constant within the isothermal enclosure of the fuel cell, or Faradaic reformer, whereas other writers put reactants in, and take products out, at standard conditions. 

The analyses here differ from those of Gardiner (1996), Kotas (1995) and Moran and Shapiro (1993) because of the use of the fugacity calculations from the JANAF tables (Chase etal., 1998), and, more importantly, because the contents of the isothermal enclosure of the fuel cell are at concentrations determined by the equilibrium constant (high vacuum of reactants, high concentration of products). The introduction of a Faradaic reformer is new. 

Consider a small body of surface area A, emissivity c. and absorptivity a at temperature T contained in a large isothermal enclosure at the same temperature, as shown in Fig. 12-35. Recall that a huge isothermal enclosure forms a blackbody cavity regardless of the radiative properties of the enclosure surface, and the body in the enclosure is too small to interfere with the blackbody nature of the cavity. Therefore, the radiation incident on any part of the surface of the small body is equal to the radiation emitted by a blackbody at temperature 7. That is, G = Ei, T) - trT", and the radiation absorbed by the small body pet unit of its surface area i.s... 

Blackbody radiation is achieved in an isothermal enclosure or cavity under thermodynamic equilibrium, as shown in Figure 7.4a. A uniform and isotropic radiation field is formed inside the enclosure. The total or spectral irradiation on any surface inside the enclosure is diffuse and identical to that of the blackbody emissive power. The spectral intensity is the same in all directions and is a function of X and T given by Planck s law. If there is an aperture with an area much smaller compared with that of the cavity (see Figure 7.4b), X the radiation field may be assumed unchanged and the outgoing radiation approximates that of blackbody emission. All radiation incident on the aperture is completely absorbed as a consequence of reflection within the enclosure. Blackbody cavities are used for measurements of radiant power and radiative properties, and for calibration of radiation thermometers (RTs) traceable to the International Temperature Scale of 1990 (ITS-90) [5]. 

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. 

Radiation within an isothermal enclosure with blackbody boundaries is isotropic that is, uniform in all directions. 

We can derive a relationship between the absorptivity a, and emissitivy of a material by placing this material in an isothermal enclosure and allowing the body and enclosure to reach the same temperature at thermal equilibrium. If G is the irradiation on the body, the energy absorbed must equal the energy emitted. 

There are several reasons why power measurements made on this basis may still suffer from systematic errors. For example, the assumption has been made that the beam does not diffract significantly within the isothermal enclosure, and that the reflectance of the disc is indeed small so that no standing waves are set up. It is also evident from Fig. 4.1 that there is a systematic difference between the microwave data and the (sub)mm data at wavelengths up to 447 /tm, these sets of data having been obtained using different procedures. Finally, one has to assume that individual calorimeters all have the same behaviour, which might not be true if, for example, the precise thickness of various layers in the thermopile is crucial. 

Currently, high temperature mass spectrometry is one of the most powerful methods in high temperature chemistry. A particular feature of this method is a high temperature molecular beEim source, namely a Knudsen (or effusion) cell. A Knudsen cell is an isothermal enclosure with a small orifice of precisely... 

Suppose that this isothermal instrument views a 200 K blackbody. The detector sees only objects of its own temperature. The motion of the interferometer mirror inside this perfectly isothermal enclosure caimot affect the net flux at the detector the interferogram must be zero. Consequently, the amplitude A2(v), which is the Fourier component for wavenumber v of the interferogram, must also be zero and Eq. (5.13.12) simplifies to... 

If the kiln may be considered an enclosure bounding an isothermal gray gas of emissivity, S, with two bounding surfaces consisting of reradiating walls of area, and of bed soHds (the radiation sink) of area, then the expression for R becomes (19)... 

In industrial appHcations it is not uncommon that the thermocouple must be coupled to the readout instmment or controUer by a long length of wire, perhaps hundreds of feet. It is obvious from the differential nature of the thermocouple that, to avoid unwanted junctions, extension wine be of the same type, eg, for a J thermocouple the extension must be type J. Where the thermocouple is of a noble or exotic material, the cost of identical lead wine may be prohibitive manufacturers of extension wine may suggest compromises which are less costiy. Junctions between the thermocouple leads and the extension wine should be made in an isothermal environment. The wine and junctions must have the same electrical integrity as the thermocouple junction. Because the emf is low, enclosure in a shield or grounded conduit should be considered. 

Sin e-Gas-Zone/Two-Surface-Zone Systems An enclosure consisting of but one isothermal gas zone and two gray surface zones can, properly specified, model so many industrially important radiation problems as to merit detailed presentation. One can evaluate the total radiation flux between any two of the three zones, including multiple reflec tion at all surfaces. 

Isothermal DSC measurements were made with a Perkin Elmer DSC-2C apparatus, modified for UV irradiation (Figure 1). The aluminum sample holder enclosure cover contains two windows, one for the sample and one for the reference compartment. The windows consist of cylindrical quartz cuvettes which have been evacuated in order to prevent moisture condensation. The windows were mounted by using a thermally cured epoxy adhesive. 

B Edwards, D. K. Radiation Interchange in a Nongray Enclosure Containing an Isothermal Carbon Dioxide-Nitrogen Gas Mixture, J. Heat Transfer, vol. 84, p. 1, 1962. 

Consider an arbitrary three-dimensional enclosure of total volume V and surface area A which confines an absorbing-emitting medium (gas). Let the enclosure be subdivided (zoned) into M finite surface area and N finite volume elements, each small enough that all such zones are substantially isothermal. The mathematical development in this section is restricted by the following conditions and/or assumptions ... 

The standard hemispherical monochromatic gas emissivity is defined as the direct volume-to-surface exchange area for a hemispherical gas volume to an infinitesimal area element located at the center of the planar base. Consider monochromatic transfer in a black hemispherical enclosure of radius ft that confines an isothermal volume of gas at temperature Tg. The temperature of the bounding surfaces is T. Let A2 denote the area of the finite hemispherical surface and dAi denote an infinitesimal element of area located at the center of the planar base. The (dimensionless) monochromatic direct exchange area for exchange between the finite hemispherical surface A2 and d then follows from direct integration of Eq. (5-116a) as... 

An inclined rectangular enclosure with isothermal surfaces. 

Fig. 5.22 Isothermal hollow enclosure for the realisation of a black body. 1 insulation 2 heating 3 copper cylinder 4 reflected radiation 5 polished surface 6 black surface 7 incident beam 8 strongly absorbing surface...

We will now consider a hollow enclosure surrounded by walls consisting of several parts each with an isothermal surface, Fig. 5.55. According to H.C. Hottel... 

If the bodies participating in radiative exchange cannot be assumed to be black bodies, then the reflected radiation flows also have to be considered. In hollow enclosures, multiple reflection combined with partial absorption of the incident radiation takes place. A general solution for radiative exchange problems without simplifying assumptions is only possible in exceptional cases. If the boundary walls of the hollow enclosure are divided into isothermal zones, like in 5.5.2, then a relatively simple solution is obtained, if these zones behave like grey Lambert radiators. Each zone is characterised purely by its hemispherical total emissivity si — whilst at = is valid for its absorptivity, and for the reflectivity... 

We will now investigate radiative exchange between the isothermal walls (zones) of the enclosure illustrated in Fig. 5.57. The temperature of some of the zones is known, for others the heat flow supplied from or released to the outside is given. The heat flows of the zones with known temperatures and the temperature of each zone with stipulated heat flow are what we are seeking. There are as many unknown quantities (temperatures or heat flows) as there are zones. 

Fig. 5.57 Hollow enclosure bounded by isothermal surfaces (zones) each of which is a grey Lambert radiator...

An enclosure surrounded by three isothermal surfaces (zones), like that shown schematically in Fig. 5.59, serves as a good approximation for complicated cases of radiative exchange. Zone 1 at temperature 7 and with emissivity is the (net-) radiation source, it is supplied with a heat flow Q1 from outside. Zone 2 with temperature T2 < Tx and emissivity e2 is the radiation receiver, whilst the third zone at temperature TR, assumed to be spatially constant, is a reradiating wall, (Qr = 0). The heat flow Qi = — Q2 transferred by radiative exchange in the enclosure is to be determined. 

This result holds in particular for concentric spheres and very long concentric cylinders as here the assumption of isothermal surfaces applies more easily. If, however, body 1 lies eccentric in the enclosure surrounded by body 2, Fig. 5.64, then the two surfaces will generally not be isothermal, as the radiation flow is much higher in the regions where the two surfaces are close to each other than where a large distance exists between them. 

In complicated geometries the boundary walls of an enclosure must be divided into several zones. Non-isothermal walls also have to be split into a number of isothermal surfaces (= zones) in order to increase the accuracy of the results13. The equivalent electrical circuit diagram introduced in 5.5.3.2 would be confusing for this case. It is more sensible to set up and then solve a system of linear equation for the n radiosities of the n zones. The difficulty here is not the solving of the large number of equations in the system, but is the determination of the n2 view factors that appear. 

The radiative exchange in a gas filled enclosure is more difficult to calculate than the exchange dealt with in 5.5.3, without an absorbing and therefore self radiating gas. In the following we will consider two simple cases, in which an isothermal gas is involved in radiative interchange with its boundary walls that are likewise at a uniform temperature. At the end of this section we will point to more complex methods with which more difficult radiative exchange problems may be solved. 

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