Isothermal changes, reversible thermodynamics

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. 

Finally let these molecules of C and D change into A and B in reservoir I, no work being done in either equilibrium box dunng the cycle as s whole The cycle is now completed, the initial conditions being re stored Since this has been done isothermally and reversibly it follows from the Second Law of Thermodynamics that no work on the whole has been done That is—... 

During the reversible process the system undergoes a sequence of states all of which are infinitely near a true, thermodynamic equilibrium. Therefore, the reversible process can be unambiguously illustrated in a diagram, for example as a curve depicting a reversible isothermal change of state for a gas in a pV diagram. 

FIGURE 4.1 Very general system for illustrating the thermodynamics of a small, reversible, isothermal change. 

The combination of properties U - TS occurs so frequently in thermodynamic analysis that it is given a special name and symbol, namely A, the work fimction or maximum luork (because it represents the maximum work per unit mass, obtainable during any isothermal reversible change in any given system). Therefore, it is seen that... 

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. 

It is used internally and rarely enters directly into ealens, but rather in the form of its increments or changes. Entropy is arrived at in thermodynamics in the form of the conception of a change in the entropy of the system, which is equal to the heat taken up during each infinitesimal change of a reversible or isothermal process, divided by the temperature at which it is absorbed. For the entire change in the system, the change in entropy is equal to the summation of the infinitesimal terms as denoted by the equation ... 

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. 

The integral molar entropy of adsorption is obtained from a well-known thermodynamic relation for a reversible, isothermal process the heat is equal to the change in entropy multiplied by the temperature. This directly leads to... 

Consider a single homogeneous phase of one component of unchanging composition. If it undergoes an isothermal reversible change and does work, then from the first law of thermodynamics ... 

In contrast, as discussed earlier in Section 3.2.1, studies of the interfacial capacitance allow the effect of the applied potential on the adsorption thermodynamics to be elucidated. For example, as discussed above, cyclic voltammetry reveals that the dependence of the surface coverage T on the bulk concentration of 20H-AQ is accurately described by the Langmuir isotherm over the concentration range 20 nM to 2 iM. However, since adsorption is reversible in the anthraquinone system, the effect of changing the potential at which the monolayer is formed on the surface coverage, or the adsorption thermodynamics, cannot be investigated by ex situ... 

Rouquerol et al. (11, 12) have recently described the experimental determination of entropies of adsorption by applying thermodynamic principles to reversible gas-solid interactions. Theoretically, the entropy change associated with the adsorption process can only be measured in the case of reversible heat exchange. The authors showed how isothermal adsorption microcalorimetry can be used to obtain directly and continuously the integral entropy of adsorption by a slow and constant introduction of adsorbate under quasi-equilibrium conditions (11) or by discontinuous introduction of the adsorbate in an open system (12). 

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