Entropy and irreversibility

G. Lindblad. Non-Equilibrium Entropy and Irreversibility, Mathematical Physics Studies, vol. 5. D. Reidel Publishing Company, Dordrecht (1983). 

The Entropy and Irreversible Processes.—Unlike the internal energy and the first law of thermodynamics, the entropy and the second law are relatively unfamiliar. Like them, however, their best interpretation comes from the atomic point of view, as carried out in statistical mechanics. For this reason, we shall start with a qualitative description of the nature of the entropy, rather than with quantitative definitions and methods of measurement. 

ENTROPY AND IRREVERSIBILITY IN CHEMICAL REACTIONS THE CHEMICAL AFFINITY... 

J. D. Ramshaw (1986) Remarks on entropy and irreversibility in non-hamiltonian systems. Phys. Lett. A 116, p. 110... 

A closed system can only do work at the cost of an increase in entropy. And irreversible reactions can only take place in one direction, that of an increase in entropy. The reactions will continue until equilibrium is established. 

Within the past 50 years our view of Nature has changed drastically. Classical science emphasized equilibrium and stability. Now we see fluctuations, instability, evolutionary processes on all levels from chemistry and biology to cosmology. Everywhere we observe irreversible processes in which time symmetry is broken. The distinction between reversible and irreversible processes was first introduced in thermodynamics through the concept of entropy , the arrow of time as Arthur Eddington called it. Therefore our new view of Nature leads to an increased interest in thermodynamics. Unfortunately, most introductory texts are limited to the study of equilibrium states, restricting thermodynamics to idealized, infinitely slow reversible processes. The student does not see the relationship between irreversible processes that naturally occur, such as chemical reactions and heat conduction, and the rate of increase of entropy. In this text, we present a modem formulation of thermodynamics in which the relation between rate of increase of entropy and irreversible processes is made clear from the very outset. Equilibrium remains an interesting field of inquiry but in the present state of science, it appears essential to include irreversible processes as well. 

It is still necessary to consider the role of entropy m irreversible changes. To do this we return to the system considered earlier in section A2.1.4.2. the one composed of two subsystems in themial contact, each coupled with the outside tliroiigh movable adiabatic walls. Earlier this system was described as a function of tliree independent variables, F , and 0 (or 7). Now, instead of the temperature, the entropy S = +. S P will be... 

Figure A2.1.10. The impossibility of reaching absolute zero, a) Both states a and p in complete internal equilibrium. Reversible and irreversible paths (dashed) are shown, b) State P not m internal equilibrium and with residual entropy . The true equilibrium situation for p is shown dotted.

The reader is referred to the original papers for detailed analysis, where the various components of entropy generation and irreversibility are defined. The advantage of this work is not only that it involves less approximation but also that it is revealing in terms of the basic thermodynamics. It should also be used by designers who should be able to see how design changes relate to increased or decreased local loss. 

On the other hand, in any irreversible process although the system may gain (or lose) entropy and the surroundings lose (or gain) entropy, the system plus surrounding will always gain in entropy (equation 20.141). Thus for a real process proceeding spontaneously at a finite rate... 

The application of the principle of entropy to irreversible processes has given rise to much discussion and controversy. The exposition here adopted is based on the investigations of Lord Kelvin (1852) in connexion with Dissipation of Energy. 

FIGURE 7.21 The changes in entropy and internal energy when an ideal gas undergoes (a) reversible and (b) irreversible changes between the same two states, as described in Example 7.12. 

In a system undergoing a reversible adiabatic process, there is no change in its entropy. This is so because by definition, no heat is absorbed in such a process. A reversible adiabatic process, therefore, proceeds at constant entropy and may be described as isentropic. The entropy, however, is not constant in an irreversible adiabatic process. 

The entropy, Spontaneous vs non-spontaneous, Reversible and irreversible processes, Calculation of entropy changes (Isothermal, isobaric, isochoric, adiabatic), Phase changes at equilibrium, Trouton s rule, Calculation for irreversible processes... 

In order to take into account the spontaneity and irreversibility of real processes (heat always goes from a hot substance to a cold one, but not the reverse), thermodynamics invokes the notion of the entropy S. In statistical terms entropy is defined as the probability of accessible states for each molecule in the system ... 

At times t < f0 w [where f0 ° is an infinitesimal amount less than f0 ], the density is zero. Only after the pair is formed can there be any probability of its existence [499]. This is cause and effect, but strictly only applicable at a macroscopic level. On a microscopic scale, time reversal symmetry would allow us to investigate the behaviour of the pair at time and so it reflects the inappropriateness of the diffusion equation to truly microscopic phenomena. The irreversible nature of diffusion on a macroscopic scale results from the increase of entropy, and should be related to microscopic events described by the Sturm—Liouville equation (for instance) and appropriately averaged. 

THOMSON PRINCIPLE. The hypothesis that, if thermodynamically reversible and irreversible processes take place simultaneously in a system, the laws of thermodynamics may be applied to the reversible process while ignoring for this purpose the creation of entropy due to die irreversible process. Applied originally by Thomson to the case of... 

In the development of the second law and the definition of the entropy function, we use the phenomenological approach as we did for the first law. First, the concept of reversible and irreversible processes is developed. The Carnot cycle is used as an example of a reversible heat engine, and the results obtained from the study of the Carnot cycle are generalized and shown to be the same for all reversible heat engines. The relations obtained permit the definition of a thermodynamic temperature scale. Finally, the entropy function is defined and its properties are discussed. 

Having defined the entropy function, we must next determine some of its properties, particularly its change in reversible and irreversible processes taking place in isolated systems. (In each case a simple process is considered first, then a generalization.)... 

In words when a system undergoes a change, the increase in entropy of the system is equal to or greater than the heat absorbed in the process divided by the temperature. On the other hand, the equality, which provides a definition of entropy increment, applies to any reversible process, whereas the inequality refers to a spontaneous (or irreversible) process, defined as one which proceeds without intervention from the outside. Example 1 illustrates the reversible and irreversible reactions. 

We thus see that an irreversible process, if occurring at constant entropy and volume (dS = 0 and dV = 0), is accompanied by a decrease in the internal energy of the system as shown in Eq. 3.18 ... 

As mentioned above, free energy F is occasionally called the Helmholtz energy, and free enthalpy G is frequently called the Gibbs energy. These two energy functions F and G correspond to the amounts of energy that are freed from the restriction of entropy and hence can be fully utilized for irreversible processes to occur at constant temperature. 

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