Isothermal isobaric process

It might seem that, for the derivation of kinetic equations describing variations in the amounts of substance eqns. (17) and (18), the equation of state is unnecessary. But this is not so. In the case of a variable reaction volume, it may be necessary to express gas-phase substance concentrations through their amounts, since step rates w are specified as functions of concentrations. For isobaric isothermal processes and ideal gases cg = Ne/ V = PN IN otRT. 

Vapor-Compression Cycles The most widely used refrigeration principle is vapor compression. Isothermal processes are realized through isobaric evaporation and condensation in the tubes. Standard vapor compression refrigeration cycle (counterclockwise Ranldne cycle) is marked in Fig. ll-72<7) by I, 2, 3, 4. 

The IsoSiv process is an isobaric, isothermal adsorption technique used to separate n-paraffins from gas oils. The operation conditions are approximately 370°C and 100 psi. Desorption is achieved using n-pentane or n-hexane. The solvent is easily distilled from the heavier n-paraffins and then recycled. 

In an isothermal process, heat must be added during an expansion and removed during a compression to keep the temperature constant. We will describe this more fully as we now calculate the heat added or removed in isobaric, isochoric, and isothermal processes. 

We have seen how to calculate q for the isochoric and isobaric processes. We indicated in Chapter 1 that q = 0 for an adiabatic process (by definition). For an isothermal process, the calculation of q requires the application of other thermodynamic equations. For example, q can be obtained from equation (2.3) if AC and w can be calculated. The result is... 

Besides the reversible and irreversible processes, there are other processes. Changes implemented at constant pressure are called isobaric process, while those occurring at constant temperature are known as isothermal processes. When a process is carried out under such conditions that heat can neither leave the system nor enter it, one has what is called an adiabatic process. A vacuum flask provides an excellent example a practical adiabatic wall. When a system, after going through a number of changes, reverts to its initial state, it is said to have passed through a cyclic process. 

The schematic Ericsson cycle is shown in Fig. 4.27. The p-v and T-s diagrams of the cycle are shown in Fig. 4.28. The cycle consists of two isothermal processes and two isobaric processes. The four processes of the Ericsson cycle are isothermal compression process 1-2 (compressor), isobaric compression heating process 2-3 (heater), isothermal expansion process 3-4 (turbine), and isobaric expansion cooling process 4-1 (cooler). 

The largest commercial production facilities employ the isothermal-isobaric CVl process to produce mostly SiC/SiC or C/SiC composites. The hot zones of these reactors measnre 3 m or larger and can accommodate hundreds of parts. 

The isothermal processes in this cycle are also isobaric (constant pressure). The efficiency of a heat pump is defined as the ratio between the heat removed from the process (QJ and the work (W) required to accomplish this heat removal. 

Fig. n.9. Isobaric isothermal ternary phase diagram containing process paths for an asymmetric transformation example. The two enantiomers are labeled R and S, and the solvent is labeled W. 

Only the ideal cases of an isothermal-isobaric combustion process will be assumed. This combustion is superior to the usual isobaric-adiabatic process. Such an assumption can be verified more easily than in a normal combustion process, since in the cases studied here the chemical reactions take place at the surface of the oxygen carriers. 

We now present an example of MREM. We consider an isobaric-isothermal ensemble and exchange not only the temperature but also the pressure values of pairs of replicas during a MC or MD simulation [94]. Namely, suppose we have M replicas with M different values of temperature and pressure (Tm,Vm). We are setting Eo = E, V = V, and Am = Vm in (4.58). We exchange replicas i and j which are at (Tm,Vm) and (Tn,Vn), respectively. The transition probability of this replica-exchange process is then given by (4.48), where (4.60) now reads [3,80,96]... 

The successive Legendre transformations of E yield a state function, G, for which the natural variables p and T, are both intensive properties (independent of the size of the system). Furthermore, for dp = 0 and dT = 0 (isobaric, isothermal system), the state of the system is characterized by dG. This is clearly convenient for chemical applications under atmospheric pressure, constant-temperature conditions (or at any other isobaric, isothermal conditions). Then, in place of equation (21) for internal energy variation, we state the conditions for irreversible or reversible processes in terms of the Gibbs energy as... 

For an isobaric and isothermal process, the equilibrium constant K is given by... 

The analysis for ecological function is similar to power output, and also leads to similar results. The shape of function u = u(Zl, Is, e) is the same as in Equation (87), but the form of Z =Z (e, Is, A) changes. Because heating and cooling in both isochoric and isobaric processes are considered constant, and taking into account Equations (75) and (78), the change of entropy can be taken only for isothermal processes. Then, the change of entropy for the non-endoreversible cycle considered is... 

The Ericsson cycle consisting of two isobaric processes and two isothermal processes is shown in Figure 4. Now, it follows a similar procedure as in the Stirling cycle case. Thus, the hypothesis on constant heating and cooling, now at constant pressure, is expressed as... 

For isothermal/isobaric CVI processes there is no forced flow, i.e. the convection term cannot be taken into consideration. Assuming the first-order reaction, Equation (5.2) becomes... 

A change of state is called a process. A system goes through an adiabatic process if no heat exchange occurs during the change of state. An isothermal process takes place at a constant temperature, and an isobaric process occurs at constant pressure. 

The value of G(A) is equal to the work of thinning the film in a reversible, isobaric, and isothermal process from infinity to a finite thickness A, with TT(A) = —(dG/ dh)T pL ij vgi vs- Derjaguin et al. (1987) point out that the choice of 11(A) as the basic thermodynamic property is not a mere change of notation, but 11(A) has advantages in cases where Gibbs thermodynamic theory is not well defined, such as, when interfacial zones overlap to the extent that the film does not retain the intensive properties of the bulk phase. The use of the disjoining pressure is advantageous from an experimental point of view because of the relative ease to account for different contributions (e.g., electrostatic effects). 

Adiabatic processes occur without any exchange of heat between the system and its surroundings. Isothermal processes occur at constant temperature, isobaric processes at constant pressure, isochoric at constant volume, and isoplethal at constant composition. Finally, in a cyclical process, initial and final states of the system are identical. Integration in cyclical processes is often symbolized by the integral... 

From thermodynamic reasons follows that the change AmH of the molar (or specific or segment molar) enthalpy in an isothermal-isobaric mixing process is also the molar (or specific or segment molar) excess enthalpy, ff, of the mixture. The dependence of bf upon temperature, T, and pressure, P, permits the correlation of such data with excess heat capacities, Cf, and excess volumes,... 

Direction of corrosion process is determined by thermodynamic properties of the system. The reactivity is determined by the change in isobaric-isothermal potential or Gibbs energy... 

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