Entropy irreversible process

Fourier s law was the first example describing an irreversible process. There is a privileged direction of time as heat flows according to Fourier s law, from higher to lower temperature. This is in contrast with the laws of Newtonian dynamics in which past and future play the same role (time enters in Newton s law only through a second derivative, so Newton s law is invariant with respect to time inversion t —t). It is the Second Law of thermodynamics which expresses the difference between reversible and irreversible processes through the introduction of entropy. Irreversible processes produce entropy. 

Real Life Processes and Entropy Irreversible Processes... 

A2.1.4.7 IRREVERSIBLE PROCESSES WORK, HEAT AND ENTROPY CREATION... 

For an irreversible process, invoking the notion of entropy transfer and entropy creation, one can write... 

This completes the heuristic derivation of the Boltzmann transport equation. Now we trim to Boltzmaim s argument that his equation implies the Clausius fonn of the second law of thennodynamics, namely, that the entropy of an isolated system will increase as the result of any irreversible process taking place in the system. This result is referred to as Boltzmann s H-theorem. 

When a process is completely reversible, the equahty holds, and the lost work is zero. For irreversible processes the inequality holds, and the lost work, that is, the energy that becomes unavailable for work, is positive. The engineering significance of this result is clear The greater the irreversibility of a process, the greater the rate of entropy production and the greater the amount of energy that becomes unavailable for work. Thus, every irreversibility carries with it a price. 

Adiabatic irreversible process in which entropy is generated... 

The entropy of the system plus surroundings is unchanged by reversible processes the entropy of the system plus surroundings increases for irreversible processes. 

It must be emphasised that the heat q which appears in the definition of entropy (equation 20.137) is always that absorbed (or evolved) when the process is conducted reversibly. If the process is conducted irreversibly and the heat absorbed is q, then q will be less than q, and q/T will be less than AS the entropy change (equation 20.137). It follows that if an irreversible process takes place between the temperatures Tj and 7 , and has the same heat intake q at the higher temperature 7 2 as the corresponding reversible process, the efficiency of the former must be less than that of the latter, i.e. 

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... 

There are three different approaches to a thermodynamic theory of continuum that can be distinguished. These approaches differ from each other by the fundamental postulates on which the theory is based. All of them are characterized by the same fundamental requirement that the results should be obtained without having recourse to statistical or kinetic theories. None of these approaches is concerned with the atomic structure of the material. Therefore, they represent a pure phenomenological approach. The principal postulates of the first approach, usually called the classical thermodynamics of irreversible processes, are documented. The principle of local state is assumed to be valid. The equation of entropy balance is assumed to involve a term expressing the entropy production which can be represented as a sum of products of fluxes and forces. This term is zero for a state of equilibrium and positive for an irreversible process. The fluxes are function of forces, not necessarily linear. However, the reciprocity relations concern only coefficients of the linear terms of the series expansions. Using methods of this approach, a thermodynamic description of elastic, rheologic and plastic materials was obtained. 

In this case there is an increase of entropy in an irreversible process, whilst the energy remains constant. This result brings out clearly the independence of the two fundamental principles of thermodynamics, the first law dealing with the energy of a system of bodies, and the second law with the entropy. 

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. 

Equation (2.66) indicates that the entropy for a multipart system is the sum of the entropies of its constituent parts, a result that is almost intuitively obvious. While it has been derived from a calculation involving only reversible processes, entropy is a state function, so that the property of additivity must be completely general, and it must apply to irreversible processes as well. 

The increase in the entropy of an irreversible process may be illustrated in the following manner. Considering the spontaneous transfer of a quantity of heat 8q from one part of a system at a temperature T, to another part at a temperature 7, then the net change in the entropy of the system as a whole is then ... 

Because A.Ssllll = —AS, AStor = 0. This value is in accord with the statement that the process is reversible, (b) For the irreversible process, AS is the same, at +7.6 J K 1. No work is done in free expansion (Section 6.3), and so w = 0. Because AU = 0, it follows that q = 0. Therefore, no heat is transferred into the surroundings, and their entropy is unchanged ASslirr = 0. The total change in entropy is therefore ASt()t = +7.6 J-K. The positive value is consistent with an irreversible expansion. 

In contrast to thermodynamic properties, transport properties are classified as irreversible processes because they are always associated with the creation of entropy. The most classical example concerns thermal conductance. As a consequence of the second principle of thermodynamics, heat spontaneously moves from higher to lower temperatures. Thus the transfer of AH from temperature to T2 creates a positive amount of entropy ... 

The processes that occur at a finite rate, with finite differences of temperature and pressure between parts of a system or between a system and its surroundings, are irreversible processes. It has been shown that the entropy of an isolated system increases in every natural (i.e., irreversible) process. It may be noted that this statement is restricted to isolated systems and that entropy in this case refers to the total entropy of the system. When natural processes occur in an isolated system, the entropy of some portions of the system may decrease and that of other portions may increase. The total increment, however, is always greater than the total decrement. The entropy of a nonisolated system may either increase or decrease, depending on whether heat is added to it or removed from it and whether irreversible processes occur within it. Considered all in all, it is necessary to define clearly the system under consideration when increases and decreases in entropy are discussed. 

Hence, when Tk is zero the system is in equilibrium, but for non-zero Tk an irreversible process that takes the system towards equilibrium, occurs. The quantity Tkl which is the difference between intensive parameters in entropy representation, acts as the driving force, or affinity of the non-equilibrium process. 

The sum is equal to zero for reversible processes, where the system is always under equilibrium conditions, and larger than zero for irreversible processes. The entropy change of the surroundings is defined as... 

Diffusion of the electroactive species within the electrode toward or away from the interface with the electrolyte is an irreversible process. The sum of the products of the forces and fluxes corresponds to the entropy production. In order to avoid space charge accumulation, the motion of at least two types of charged species has to be considered for charge compensation. Onsager s equations read in the isothermal case (neglecting energy fluxes)... 

The definition of entropy requires that information about a reversible path be available to calculate an entropy change. To obtain the change of entropy in an irreversible process, it is necessary to discover a reversible path between the same initial and final states. As S is a state function, AS is the same for the irreversible as for the reversible process. 

As the same change in state occurs in the irreversible process, A5 for the hot reservoir stiU is given by Equation (6.94). During the reversible process, the reservoir Ti absorbs heat and undergoes the entropy change... 

Thus, the entropy change for an irreversible process occurring in an isolated system is greater than or equal to zero, with the equal sign applying to the limiting case of a reversible process. 

It has been suggested that biological systems may constitute exceptions to the second law of thermodynamics, because they carry out irreversible processes that result in a decrease in the entropy of the biologic system. Comment on this suggestion. 

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