Isotherms representative absorption

In contrast to isentropy, the process of isothermal compression-expansion, which is accompanied by heat release or heat absorption, is represented by an exergy vector with the slope of < 1 in the regimes of heat absorption and heat release as shown in Fig. 11.10(a). 

The usual way of representing polymer adsorption onto clay surfaces is to plot an isotherm showing the amount of polymer adsorbed in grams per gram of clay as a function of the equilibrium concentration of polymer in units of g cm 3. We have to be careful in comparing our results with standard isotherms because we are measuring the total amount of PEO inside the clay. This absorbed mass is not necessarily adsorbed onto the clay surfaces, but may be located in the interlayer solution. To reflect this difference, we have used the unusual nomenclature absorption isotherm rather than the usual adsorption isotherm in the presentation of the data. 

FIGURE 12.8 Absorption isotherm data at r = 0.1, c = 0.1 M. The closed circles and open triangles show the amount of PEO taken up by the gel for M = 18,000 (bridging), with the circles and triangles representing GPC analyses and chemical analyses, respectively the open circles are for M = 4,000 (nonbridging). 

The relationship between relative humidity and the water absorbed at equilibrium by a sample of purified wool fibers, at a fixed temperature, is sigmoid [290]. The relationship shows hysteresis (Figure 5.13). The lower curve represents the equilibrium water content (EWC) of samples of wool that were originally dry and have reached equilibrium at different relative humidities (RH). It is known as the absorption isotherm. The upper curve represents the EWC of originally wet samples that have reached equilibrium at different RHs it is the desorption isotherm. 

The rates of absorption and desorption of water by wool, and the heat changes during absorption and desorption, have been investigated extensively under different conditions, including different temperatures. Many attempts have been made to devise equations that represent the absorption isotherms of water by wool and other hydrophilic fibers [274,293]. 

The second equation represents the absorption isotherm of the system. It is a hyperbola of the shape shown in Fig. 13 which is convex to the pressure axis. The vapour pressure P of the pure volatile component is approached at njrio == oo. ... 

We can represent states of the system (with constant values specified for all the variables except 9 and at) by a set of isotherms as shown in Figure 2.1 la. Two isotherms, 9 and 92 are shown, with 92 < 9t. State I, which is defined by 9 and A], can be connected to states T and 1" by a series of reversible isothermal processes (horizontal lines in the figure). We remember that heat is absorbed or evolved along a reversible isothermal path, and we will assume that this flow of heat is a continuous function of at along the isotherms, with the absorption or liberation depending upon the direction in which at is varied. That is, suppose... 

We wish to show that no points to the leftbb of 2 on the isotherm 62 are accessible from point 1 via any adiabatic path, reversible or irreversible. Suppose we assume that some adiabatic path does exist between 1 and 2. We represent this path as a dotted curve in Figure 2.11a. We then consider the cycle I —>2 —> 1 — 1. The net heat associated with this cycle would be that arising from the last step 1 — 1, since the other two steps are defined to be adiabatic. We have defined the direction 1 — 1 to correspond to an absorption of heat, which we will call qy. From the first law, the net work vv done in the cycle, is given by w = —q, since AU for the cycle is zero. Thus, for this process, iv is negative (and therefore performed by the system), since qy is positive, having been absorbed from the reservoir. The net effect of this cycle, then, is to completely convert heat absorbed at a high temperature reservoir into work. This is a phenomenon forbidden by the Kelvin-Planck statement of the Second Law. Hence, points to the left of 2 cannot be reached from point 1 by way of any adiabatic path. 

For the following discussions, we will primarily use Kioc values from compilations published by Sabljic et al. (1995) and Poole and Poole (1999). According to these authors, the values should be representative for POM-water absorption (i.e., they have been derived from the linear part of the isotherms). Furthermore, many of the reported Kioc s are average values derived from data reported by different authors. Distinction between different sources of sorbents (e.g., soils, aquifer materials, freshwater, or marine sediments) has not been made. Nevertheless, at least for the apolar and weakly monopolar compounds, these values should be reasonably representative for partitioning to soil and sediment organic matter. 

The property changes of the fluid as it flows through the individual piec of equipment may be shown as paths on a TS diagram, as illustrated in Fig. 8-The sequence of paths represents a cycle. Indeed, the particular cycle shown a Carnot cycle. In this idealization, step 1 2 is the isothermal absorption... 

The vertical portions of the isotherms for the 25 weight % alloy, representing hydrogen uptake at constant pressure, show no variation of pressure with composition, indicating that in this slower hydrogen absorption, equilibrium of three solid phases has been reached. 

Simultaneous heat and mass transfer plays an important role in various physical, chemical, and biological processes hence, a vast amount of published research is available in the literature. Heat and mass transfer occurs in absorption, distillation extraction, drying, melting and crystallization, evaporation, and condensation. Mass flow due to the temperature gradient is known as the thermal diffusion or Soret effect. Heat flow due to the isothermal chemical potential gradient is known as the diffusion thermoeffect or the Dufour effect. The Dufour effect is characterized by the heat of transport, which represents the heat flow due to the diffusion of component / under isothermal conditions. Soret effect and Dufour effect represent the coupled phenomena between the vectorial flows of heat and mass. Since many chemical reactions within a biological cell produce or consume heat, local temperature gradients may contribute in the transport of materials across biomembranes. 

The absorption of vinyl chloride(VC) on surface-treated light-grade and nanoscale calcium carbonate was shown to obey the Langmuir isothermal equation in VC/calcium carbonate/water system. The absorption of VC on calcium carbonate was shown to increase with increase of the partial pressure of VC up to the saturation absorption and the absorption of VC on nanoscale calcium carbonate was greater than that of light-grade calcium carbonate at the same temp, and partial pressure of VC. The presence of calcium carbonate in VC suspension polymerisation system was found to influence the pressure/temp./ conversion(PTC) relationship of the reaction system. Based on the absorption of VC on calcium carbonate and VC distribution in vapour, water and polymer phases, a modified model to represent the PTC relationship of VC suspension polymerisation in the presence of calcium carbonate was proposed. 10 refs. 

Fig. 33. Changes in the carboxylate and amide IR bands with hydration. Shown are the IR absorption of the carboxylate band at 1580 cm" in the difference spectrum (O) and the sum of the absolute value of the absorption of the amide I difference band at 1645 and 1690 cm" (X). Data are shown for 38°C (top) and 27°C (bottom). Curves A, D O sorption onto strong sorption sites curves B, D2O sorption onto weak sorption sites curve C, DjO multimolecular adsorption. Curves A-C were derived from the sorption isotherm by htting data to a three-site model. Ordinate units represent percentages of the values at 0.33 h. From Careri etal. (1979b).

Perfectly isothermal systems are rare in chemical engineering practice and many processes, such as distillation, gas absorption, stripping, condensation, and evaporation, involve the simultaneous transfer of mass and energy across fluid-fluid interfaces. Representative temperature profiles in some nonisothermal processes are shown in Figure 11.1. The temperature profile also has a large influence in chemically reacting systems. For nonisothermal systems it is important to consider simultaneous heat transfer even though we are primarily interested in the mass transfer process. 

Figure 12.9 Illustration of the effect of thermal spiking to 140 °C on the moisture absorption of a Fibredux 927C unidirectional laminate in 96% RH at 50 °C. The individual points represent the actual moisture content immediately before and after a thermal spike. The continuous line is for the isothermal control under identical humid conditions.

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