Isothermal process reversible

We now turn specifically to the thermodynamics and kinetics of reactions (5. EE) and (5.FF). The criterion for spontaneity in thermodynamics is AG <0 with AG = AH - T AS for an isothermal process. Thus it is both the sign and magnitude of AH and AS and the magnitude of T that determine whether a reaction is thermodynamically favored or not. As usual in thermodynamics, the A s are taken as products minus reactants, so the conclusions apply to the reactions as written. If a reaction is reversed, products and reactants are interchanged and the sign of the AG is reversed also. 

Our problem is to determine how the changes of total and free energy, AU and A P, or, what are the same, the heat absorption at constant configuration and the maximum work, Qx and At, of an isothermal and reversible process, alter with the temperature of execution of the process. 

Let the change of configuration be annulled at the infinitesimally higher temperature T + ST by an isothermal reversible process so that all the normal configuration variables recover the initial values (a). This is a second isothermal process. 

If we draw the two isochores imiii, i 2< 2, on the indicator diagram (Fig. 14), all the paths of change must lie within these limits, which fix the range or amplitude of the process. Let the initial state ( i, T) be a, and let the gas expand isothermally and reversibly to a the maximum work AT is represented by the area aa vtf i, which is shown later to be ... 

We shall now prove that P, for fixed values of 7r and the temperature, is definite for a given solution. For this purpose we have first of all to show that the dilution or concentration of the solution can be effected isothermally and reversibly. If the above apparatus is constructed of some good conductor of heat, placed in a large constant-temperature reservoir, and if all processes are carried out very slowly, the isothermal condition is satisfied. Further, suppose the end pistons fixed, and then apply to the septum an additional small pressure SP towards the solution. There will be a slight motion of the septum, through a small volume SV, and work... 

The thermodynamic aspect of osmotic pressure is to be sought in the expenditure of work required to separate solvent from solute. The separation may be carried out in other ways than by osmotic processes thus, if we have a solution of ether in benzene, we can separate the ether through a membrane permeable to it, or we may separate it by fractional distillation, or by freezing out benzene, or lastly by extracting the mixture with water. These different processes will involve the expenditure of work in different ways, but, provided the initial and final states are the same in each case, and all the processes are carried out isothermally and reversibly, the quantities of work are equal. This gives a number of relations between the different properties, such as vapour pressure and freezing-point, to which we now turn our attention. 

We shall now calculate the diminution of free energy which results from the admixture of Ni mols of [1] and N2 mols of [2], both in the liquid state. The simplest method is an application of equation (13) of 52, which states that the work done in the isothermal and reversible execution of a process is equal to the diminution of free energy ... 

Since the process is isothermal and reversible, we may apply the equation of 58 as a special case of the Second Law ... 

The agreement is remarkably good, which shows that the lead accumulator is almost theoretically reversible, and the example is all the more interesting in that it contains direct measurements of the maximum work (i.e., the diminution of free energy) of an isothermal process carried out in two entirely different ways. 

We can represent states of the system (with constant values specified for all the variables except 9 and at) by a set of isotherms as shown in Figure 2.1 la. Two isotherms, 9 and 92 are shown, with 92 < 9t. State I, which is defined by 9 and A], can be connected to states T and 1" by a series of reversible isothermal processes (horizontal lines in the figure). We remember that heat is absorbed or evolved along a reversible isothermal path, and we will assume that this flow of heat is a continuous function of at along the isotherms, with the absorption or liberation depending upon the direction in which at is varied. That is, suppose... 

It is useful to compare the reversible adiabatic and reversible isothermal expansions of the ideal gas. For an isothermal process, the ideal gas equation can be written... 

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. 

In making diagrams of various reversible cycles, it is a common practice to plot pressure as a function of volume because the area under the curve, JPrfV, gives the negative of the work performed in any step. Instead, we have used temperamre and volume as coordinates because a diagram on this basis emphasizes the constancy of temperamre in an isothermal process. However, it has the disadvantage that the... 

Then from the entropy change in a reversible, isothermal process [Equation (6.72)]... 

An ideal reciprocating Stirling refrigeration cycle is shown in Fig. 6.30. It is the reversible Stirling heat engine cycle, which is composed of two isothermal processes and two isochoric processes. Working fluid is... 

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 ... 

The figure usually given for reversible work of separation is for an isothermal process. Because some of the actual processes under consideration are by no means isothermal, one is left in some doubt as to whether the comparison between the actual work requirement and the isothermal reversible work is a legitimate one. Therefore in... 

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... 

S diagram the heat diagram for the process. As shown in Fig. 2, on a heat diagram, horizontal lines are reversible isothermal processes, whereas vertical lines are reversible adiabatic (isentropic) processes. 

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