Reversible Temperature Changes

The reversible expansion of a gas (a reversible flow of work) requires that the pressure of the gas differ only infinitesimally from the pressure of the surroundings. Similarly, a reversible flow of heat requires that the temperature of the system differ only infinitesimally from the temperature of the surroundings. If the temperature of the system is to change by a finite amount, then the temperature of the surroundings must change infinitely slowly. Thus, the reversible flow of heat, like the reversible expansion of a gas, is a limiting case that can be approached as closely as desired, but it can never be reached. 

If an isobaric temperature change is carried out reversibly, the heat exchanged in the process can be substituted into the expression for the entropy change, and the equations at constant pressure when no work is performed other than PV work are 

If the system is heated reversibly, the change in the surroundings is equal and opposite in sign to that for the system, and 

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The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. 

The electric polarization P and the entropy S of the crystal depend on the same quantities AT. A reversible temperature change AT implies an entropy... 

In a reversible heating, an infinitesimal temperature difference dT between the system and its surroundings is assumed during the process. Therefore, in each step of the process, the system will be infinitely close to thermal equilibrium. For a reversible temperature change developing at constant pressure p, we obtain according to (3.15) and (3.16)... 

The entropy increase A5 i.2 by a reversible temperature change from T to T2 is now calculated from (4.14)... 

Using the data in Table 3.1 and the heat capacity expression = CpdT, find the entropy change for a sample of 1.0 mol of oxygen that undergoes an isobaric reversible temperature change from 300 to 400 K. 

In case of hysteresis due to the non-equilibrium state of the system, we can give the following qualitative explanations. Modifications of the system properties are dependent on the level of its non-equilibrium state, which can be different for direct and reverse temperature changes. However, the properties of the above described rheological experiment, which showed hysteresis, were measured only after a long exposure of the system after each change of the temperature, until all relaxation processes were completed t] did not depend on exposure time Xr > Xr " ), but hysteresis did not disappear. Hence, it is impossible to explain this phenomenon by the kinetic non-equilibrium of the system. 

No polymer is ever 100% crystalline at best, patches of crystallinity are present in an otherwise amorphous matrix. In some ways, the presence of these domains of crystallinity is equivalent to cross-links, since different chains loop in and out of the same crystal. Although there are similarities in the mechanical behavior of chemically cross-linked and partially crystalline polymers, a significant difference is that the former are irreversibly bonded while the latter are reversible through changes of temperature. Materials in which chemical cross-linking is responsible for the mechanical properties are called thermosetting those in which this kind of physical cross-linking operates, thermoplastic. 

Chemical stabilization involves removing the concentration of surface hydroxyls and surface defects, such as metastable three-membered rings, below a critical level so that the surface is not stressed by rehydroxylation in use. Thermal stabilization involves reducing the surface area sufficiently to enable the material to be used at a given temperature without reversible stmctural changes. The mechanisms of thermal and chemical stabilization are interrelated because of the extreme effects that surface hydroxyls and chemisorbed water have on stmctural changes. Full densification of gels, such as the... 

Then, for any reversible structural change at constant uniform temperature and pressure... 

The absorption occurs as a result of the driving force of the partial pres-Miie from the gas to the liquid. The reactions involved are reversible bv changing the system temperature or pressure, or both. Therefore, die at[ueous base solution can be regenerated and thus circulated in a contin nous cycle. The majority of chemical solvent processes use either an amine or carbonate solution. 

These reactions are reversible by changing the system temperature. ME A also reacts with carbonyl sulfide (COS) and carbon disulfide (CSi) to form heat-stable salts that cannot be regenerated. At temperatures above 245°F a side reaction with CO2 exists that produces oxazolidone-2. a heat-stable salt, and consumes MEA from the process. 

With increasing water content the reversed micelles change via swollen micelles 62) into a lamellar crystalline phase, because only a limited number of water molecules may be entrapped in a reversed micelle at a distinct surfactant concentration. Tama-mushi and Watanabe 62) have studied the formation of reversed micelles and the transition into liquid crystalline structures under thermodynamic and kinetic aspects for AOT/isooctane/water at 25 °C. According to the phase-diagram, liquid crystalline phases occur above 50—60% H20. The temperature dependence of these phase transitions have been studied by Kunieda and Shinoda 63). 

They can often be reversed by changing the temperature or pressure. 

The equation (16) shows that the increase of bound energy in a reversible isothermal change is equal to the increase of entropy multiplied by the absolute temperature, so that the entropy may be regarded as the capacity for bound energy in such changes. B will evidently contain the arbitrary term / IT. 

Interesting phenomena are observed by increasing the concentration of reversed micelles, changing the temperature or pressure, applying high electric fields, or adding suitable solutes, In some conditions, in fact, a dramatic increase in some physicochemical properties has been observed, such as viscosity, conductance, static permittivity, and sound absorption [65,80,173,233,243,249,255,264-269],... 

Table VIII demonstrates the inverse relationship of conversion to S02 concentration in the feed that is a consequence of applying flow reversal to S02 oxidation using a single reactor. As the S02 concentration in the table moves from 0.8 to over 8 vol%, the conversion drops from 96-97% down to 85%. At the same time, the maximum bed temperature changes from 450 to 610°C. For an equilibrium-limited, exothermic reaction, this behavior is explained by variation of the equilibrium conversion with temperature.

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