Reversible constant volume processes thermodynamics

One should not conclude from Eq 4.2-7 that the reversible work for any process is equal to the change in Helmholtz energy, since this result was derived only for an isothermal, constant-volume process. The value of VK , and the thermodynamic functions to which it is related, depends on the constraints placed on the system during the change of state (see Problem 4.3). For example, consider a process occurring in a closed system at fi.xed temperature and pressure. Here we have... 

Gases behave differently from liquids and must be characterized by an equation of state. Polytropic processes are studied in thermodynamics (Saad, 1966). Essentially, pv = constant, say C, where v is the specific volume also the index n of the proeess may vary from -oo to -too. For constant pressure processes, n = 0 for isothermal processes assuming perfect gases, n = 1. For reversible adiabatic processes, n = Cp/Cv, where Cp is the specific heat at constant pressure and Cv is the value obtained at constant volume. Finally, for constant volume processes, n = co. 

The discussion given above has referred in particular to isothermal changes, but reversible processes are not necessarily restricted to those taking place at constant temperature. A reversible path may involve a change of temperature, as well as of pressure and volume. It is necessary, however, that the process should take place in such a manner that the system is always in virtual thermodynamic equilibrium. If the system is homogeneous and has a constant composition, two thermodynamic variables, e.g., pressure and volume, will completely describe its state at any point in a reversible process. 

Hence, at least for fast irreversible reactions, by (6.2.113) the loss of exergy is enormous whatever be the arrangement of the process. Classical thermodynamics knows still another hypothetical device in addition to the reversibly-working Camot cycles, viz. the reversible galvanic (electrochemical) cell. In this device, with constant volume the electric work (say) equals the affinity of the reaction, per unit integral reaction rate. Thus considering the cell working at temperature Tq with pure species, we have... 

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. 

A chemical relaxation technique that measures the magnitude and time dependence of fluctuations in the concentrations of reactants. If a system is at thermodynamic equilibrium, individual reactant and product molecules within a volume element will undergo excursions from the homogeneous concentration behavior expected on the basis of exactly matching forward and reverse reaction rates. The magnitudes of such excursions, their frequency of occurrence, and the rates of their dissipation are rich sources of dynamic information on the underlying chemical and physical processes. The experimental techniques and theory used in concentration correlation analysis provide rate constants, molecular transport coefficients, and equilibrium constants. Magde" has provided a particularly lucid description of concentration correlation analysis. See Correlation Function... 

CARNOT CYCLE. An ideal cycle or four reversible changes in the physical condition of a substance, useful in thermodynamic theory. Starting with specified values of die variable temperature, specific volume, and pressure, the substance undergoes, in succession, an isothermal (constant temperature) expansion, an adiabatic expansion (see also Adiabatic Process), and an isothermal compression to such a point that a further adiabatic compression will return the substance to its original condition. These changes are represented on the volume-pressure diagram respectively by ub. he. ctl. and da in Fig. I. Or the cycle may he reversed ad c h a. 

Consequently, the energy of the gas is constant for the isothermal reversible expansion or compression and, according to the first law of thermodynamics, the work done on the gas must therefore be equal but opposite in sign to the heat absorbed by the gas from the surroundings. For a reversible process the pressure must be the pressure of the gas itself. Therefore, we have for the isothermal reversible expansion of n moles of an ideal gas between the volumes F and V... 

The equilibrium pressure part is given by the state equation, see (2.33), (2.32). This, in fact equilibrium pressure in reversible processes, forms the whole pressure (2.6)s of the classical thermodynamic model A (density of uniform body with constant mass is given by its volume V). 

In general, the thermodynamic definition of entropy (Equations 8.6 to 8.8) yields the same value for the entropy change of a process as Boltzmann s statistical definition (Equation 8.3) for the same process. Consider, for example, the entropy change in the reversible and isothermal (constant teinperature) mmqn n i n i les of an ideal gas from an initial volume Vi to a inB39B9tft0-6K ile heat... 

The process of measurement of volume expansivity cannot be isobaric in practice. When materials expand, the root mean square velocity of the molecules increases. For the materials with negative coefficient of thermal expansion when materials expand, the root mean square velocity of molecules is expected to decrease. In either case, forcing such a process as isobaric is not a good representation of theory with experiments. Such processes can even be reversible or isentropic. Experiments can be conducted in a careful manner and the energy needed supplied or energy released removed, as the case may be, in a reversible manner. Hence, it is proposed to define volume expansivity at constant entropy. This can keep the quantity per se from violating the laws of thermodynamics. 

Because work is done when changing the area of a surface, we should be able to correlate this work to one of the thermodynamic state functions. Recall that we found in an earlier chapter that the Gibbs energy is equal to the maximum amount of non-pV work that a process could do. Because changing the area of a surface is not pressure-volume work (just like electrical work isn t pressure-volume work), then surface-tension-area work must be related to the Gibbs energy. For a reversible change in surface area that occurs at constant temperature and pressure, we have... 

It is found experimentally that the stretching of a mbber object approximately obeys three properties (1) the volume remains constant (2) the tension force is proportional to the absolute temperature and (3) the energy is independent of the length at constant temperature. An ideal rubber exactly conforms to these three properties. Since the volume is constant, the first term on the right-hand side of Eq. (28.9-1) vanishes for an ideal rubber. For reversible processes in a closed system made of ideal mbber, the first and second laws of thermodynamics give the relation ... 

Under the given process conditions, i.e. constant (T,p) and volume work as the sole work contribution, this can be expressed verbally as follows. Any spontaneous process will reduce the free energy G in a thermodynamic system in reversible processes the free energy of the system is unchanged. The free energy G cannot increase spontaneously. 

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