Entropy irreversibility

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... 

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... 

This is frequently stated for an isolated system, but the same statement about an adiabatic system is broader.) A2.1.4.6 IRREVERSIBLE CHANGES AND THE MEASUREMENT OF ENTROPY... 

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... 

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.

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. 

The total heat released is the sum of the entropy contribution plus the irreversible contribution. This heat is released inside the battery at the reaction site. Heat release is not a problem for low rate appHcations however, high rate batteries must make provisions for heat dissipation. Failure to accommodate heat can lead to thermal mnaway and other catastrophic situations. 

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. 

Thermodynamic Analyses of Cycles The thermodynamic quahty measure of either a piece of equipment or an entire process is its reversibility. The second law, or more precisely the entropy increase, is an effective guide to this degree of irreversibility. However, to obtain a clearer picture of what these entropy increases mean, it has become convenient to relate such an analysis to the additional work that is required to overcome these irreversibihties. The fundamental equation for such an analysis is... 

The fact that shock waves continue to steepen until dissipative mechanisms take over means that entropy is generated by the conversion of mechanical energy to heat, so the process is irreversible. By contrast, in a fluid, rarefactions do not usually involve significant energy dissipation, so they can be regarded as reversible, or isentropic, processes. There are circumstances, however, such as in materials with elastic-plastic response, in which plastic deformation during the release process dissipates energy in an irreversible fashion, and the expansion wave is therefore not isentropic. 

Adiabatic irreversible process in which entropy is generated... 

If the heat transferred from the control volume is not used externally to create work, but is simply lost to the atmosphere in which further entropy is created, then Equj can be said to be equal to /quj, a lost work term, due to external irreversibility. Another form of Eq. (2.23) is thus... 

Fig. 4..S. Temperalure-entropy diagram for single-slep cooling—irreversible cycle CHT ici (after Ref. (5 ).

Fig, 4.7. Temperature-entropy diagram for two step cooling—irreversible cycle, (a) Cooling air taken at appropriate pres.sures. (b) Cooling air throttled from compres.sor exit (after Ref. 5]). 

Young and Wilcock [7] have recently provided an alternative to this simple approach. They also follow step (a), but rather than obtaining as in (b) they determine the constituent entropy increa.ses (due to the various irreversible thermal and mixing effects). Essentially, they determine the downstream state from the properties To and the entropy. v, rather than T), and po- This approach is particularly convenient if the rational efficiency of the plant is sought. The lost work or the irreversibility ( f = "lay be subtracted... 

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. 

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

For any reversible process, the sum of the changes in entropy for the system and its surroundings is zero. All natural or real processes are irreversible and are accompanied by a net increase in entropy. 

Because all real processes are irreversible as a result of friction, electrical resistance, etc., any processes involving real systems experience an increase in entropy. For such systems... 

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... 

For reven sible systems, evolution almost always leads to an increase in entropy. The evolution of irreversible systems, one the other hand, typically results in a decrease in entropy. Figures 3.26 and 3.27 show the time evolution of the average entropy for elementary rules R32 (class cl) and R122 (class c3) for an ensemble of size = 10 CA starting with an equiprobable ensemble. We see that the entropy decreases with time in both cases, reaching a steady-state value after a transient period. This dc crease is a direct reflection of the irreversibility of the given rules,... 

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