Isobaric pressure, reversible

Assume a system containing 5.00 mol of ideal gas at the pressure 101325 Pa. In its initial state (1), the gas temperature is 100 °C. By an isobaric and reversible cooling, the gas temperature is reduced to 0 °C in the final state (2). The molar heat capacity of the gas Cp = 20.8 J/molK is assumed to be constant. Calculate the change in the internal energy AU of the system during the process ... 

Thus, in a reversible process that is both isothermal and isobaric, dG equals the work other than pressure-volume work that occurs in the process." Equation (3.96) is important in chemistry, since chemical processes such as chemical reactions or phase changes, occur at constant temperature and constant pressure. Equation (3.96) enables one to calculate work, other than pressure-volume work, for these processes. Conversely, it provides a method for incorporating the variables used to calculate these forms of work into the thermodynamic equations. 

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. 

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... 

The Gibbs free energy change during a reaction is a measure of the reversible work (other than pressure-volume work) that can be obtained from the process at constant T and p. Since cellular processes are isothermal and isobaric, free energies are the quantities of choice in studying metabolic processes with respect to their ability to carry out the work of cells. 

A certain gas obeys the equation of state P(V -nb) - nRT and has a constant volume heat capacity, Cv, which is independent of temperature. The parameter b is a constant. For 1 mol, find W, AE, Q, and AH for the following processes (a) Isothermal reversible expansion. (b) Isobaric reversible expansion. (c) Isochoric reversible process, (d) Adiabatic reversible expansion in terms of Tlf Vlt V2, Cp, and Cv subscripts of 1 and 2 denote initial and final states, respectively. (c) Adiabatic irreversible expansion against a constant external pressure P2, in terms of Plf P2, Tj, and 7 = (Cp/Cy). 

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... 

Recall from Section 12.1 that a true reversible process is an idealization it is a process in which the system proceeds with infinitesimal speed through a series of equilibrium states. The external pressure therefore, can never differ by more than an infinitesimal amount from the pressure, P, of the gas itself. The heat, work, energy, and enthalpy changes for ideal gases at constant volume (called isochoric processes) and at constant pressure (isobaric processes) have already been considered. This section examines isothermal (constant temperature) and adiabatic (q = 0) processes. 

The analogous result for the entropy change of the system in a reversible isobaric process (constant pressure) is... 

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). 

Thus enthalpy is a potential for (reversible) work in a constant S, P process, and will always decrease in spontaneous processes in such systems, only PAV work being allowed. Again, the fact that H is a potential for (isobaric, reversible) work is almost self-evident from looking at equation (5.27), since PAV is the maximum pressure-volume work available and AU is tlie rest of the energy change available. In fact, the restriction of constant entropy is not necessary for H to be a work potential. If AS is not zero, the amount of energy available for work will be reduced but still maximized in a reversible process. 

Txy diagrams have entirely analogous rules, but just be aware that the graph is "reversed" somewhat in shape. It s somewhat harder to calculate even in an ideal case, requiring an iterative solution, but is more useful for isobaric (constant-pressure) systems and is worth the effort. The extreme ends of the txy diagram are the boiling temperatures of pure toluene (xb = 0) and benzene (xb = 1) at 760 mmHg. 

These class II derivatives are extensive measurable state functions. Both and Cp are always positive, so U (H) always increases with isometric (isobaric) increases in T. The heat capacities are experimentally accessible by measuring the temperature change that accompanies addition of a small amount of energy (such as heat) to a system at constant volume, to yield C , or reversibly at constant pressure, to yield Cp that is. 

Consider a container filled with a one-phase multicomponent mixture of composition x the container is immersed in a reservoir that imposes its temperature T and pressure P on the mixture. The container is fitted with a single inlet by which more material can be reversibly injected, as shown schematically in Figure 3.9. The process considered here is addition to the container of a small amount of pure component 1. The reversible work associated with this process is given by (3.7.14) for an isobaric injection of material through one inlet with no outlets, (3.7.14) reduces to... 

So, when we choose the pure-substance reference state to be at the same temperature and pressure as the mixture, then the activity of component i is simply related to the reversible isothermal-isobaric work involved in adding a small amount of pure i to the mixture. This provides a physical interpretation for the activity. 

Although initially the mole fraction of solute in the vapor phase falls rapidly as the pressure is increased, this process reverses as the critical region is approached. At the critical end point temperature. Fig. 8c, the solubility increases strongly, with an infinite slope dx/dP for the isotherm. It likewise decreases with infinite slope dx/dT on an isobar passing through... 

Consider a reversible isobaric heating process of a pure substance while it exists in a single phase. The definition of heat capacity as q/ 6T (Eq. 3.1.7) allows us to substitute Cp 6.T for q, where Cp is the heat capacity of the phase at constant pressure. 

The reverse is rarely possible a decrease in molecule concentration of the interfadal volume leading to an isobaric increase of total volume and thus the interfadal tension increases at higher process pressures. A known example is represented by the interfadal tension between helium and water [16]. 

A closed thermodynamic system contains 3 mol of ideal gas at the pressure p = 1.000 atm. Dming a reversible, isobaric heating, an amount of heat Q = 482 J is supplied to the system so that the gas temperatme is increased from 21.5 °C to 28.8 °C. Prom this information, calculate a) the increase in internal energy of the system AU (J) b) the increase in enthalpy of the system AH (J) c) the molar heat capacity of the gas Cp (J/molK) d) the molar heat capacity of the gas cy (J/molK) ... 

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