Cyclic processes reversible

Flere the subscripts and/refer to the initial and final states of the system and the work is defined as the work perfomied on the system (the opposite sign convention—with as work done by the system on the surroundings—is also in connnon use). Note that a cyclic process (one in which the system is returned to its initial state) is not introduced as will be seen later, a cyclic adiabatic process is possible only if every step is reversible. Equation (A2.1.9), i.e. the mtroduction of t/ as a state fiinction, is an expression of the law of conservation of energy. 

Theorem.—The work done in any isothermal reversible cyclic process is zero (J. Moutier, 1875). 

For if a cyclic process could be performed in a heat reservoir of uniform temperature so as to give out work, it would constitute a perpetanm mobile of the second kind, the existence of which is denied by the second law. And if the cyclic process absorbed work when performed at a uniform temperature, it would, by reason of its reversibility, give out an equal amount of work when reversed this would, however, be the case first considered. Hence the production of work in either cycle is impossible, which establishes the theorem. 

If any cyclic process is performed with a given material system, the entropy of all the surrounding bodies which have in any way been involved in the process, either as emitters or absorbers of heat, either remains unchanged, if the cycle is reversible, or else increases, if the cycle is performed irreversibly. 

For this purpose we suppose the following reversible cyclic process executed. This process, it will be seen, is not a Carnot s cyclic process, but is of another type. 

Figure 2.10 (a) A schematic Carnot cycle in which isotherms at empirical temperatures 6 and 62 alternate with adiabatics in a reversible closed path. The enclosed area gives the net work produced in the cycle, (b) The area enclosed by a reversible cyclic process can be approximated by the zig-zag closed path of the isothermal and adiabatic lines of many small Carnot cycles. 

Consider any reversible cyclic process that involves the exchange of heat and work. Again, the net area enclosed by the cycle on a p-V plot gives the work. This work can be approximated by taking the areas enclosed within a series of Carnot cycles that overlap the area enclosed by the cycle as closely as possible as shown in Figure 2.10b. For each of the Carnot cycles, the sum of the q/T terms... 

Figure 3.4 Carnot cycle for the expansion and compression of an ideal gas. Isotherms alternate with adiabats in a reversible closed path. The shaded area enclosed by the curves gives the net work in the cyclic process.

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. 

Scientists call this chemical circle of life the nitrogen cycle. There are, as you know, similar, equally important cyclic processes in nature. Each process involves reversible changes changes that may proceed in either direction, from reactants to products or from products to reactants. 

Furthermore, in the four steps of the cycle (Fig. 6.8) three are adiabatic (one irreversible, two reversible). Hence, Qcycie is identical with Q of the isothermal step, that is, Q of Equation (6.104). If g > 0, then W < 0 that is, work would have been performed by the system. In other words, if Q were positive, we would have carried out a cyclical process in which heat at a constant temperature had been converted completely into work. According to the Kelvin-Planck statement of the second law, such a process cannot be carried out. Hence, Q cannot be a positive number. As Q must be either negative or zero, it follows from Equation (6.104) that... 

In contrast to thermal electron-transfer processes, the back-electron transfer (BET) (kbet) in the PET is generally exergonic as well. The apparent contradiction can be resolved by the cyclic process excitation-electron transfer-back-electron transfer in which the excitation energy is consumed. The back-electron transfer is not the formal reverse reaction of the photoinduced-electron-transfer step and so not necessarily endergonic. This has different influences on PET reactions. On the one hand, BET is the reason for energy consumption and low quantum yields. On the other hand, it can cause more complex reaction mechanisms if the... 

The PCR is a three-step cyclic process that repeatedly duplicates a specific DNA sequence, contained between two oligonucleotide sequences called primers (154,155). The two primers form the ends of the sequence of DNA to be amplified and are normally referred to as the forward and reverse primers. The forward primer is complementary to the sense strand of the DNA template and is extended 5 to 3 along the DNA by DNA polymerase enzyme (Fig. 27). The reverse primer is complementary to the antisense strand of the DNA template and is normally situated 200-500 base pairs downstream from the forward primer, although much longer sequences (up to 50 kbase) can now be amplified by PCR. The process employs a thermostable DNA polymerase enzyme (such as the Taq polymerase from Thermus aqualicus BM) extracted from bacteria found in hot water sources, such as thermal pools or deep-water vents. These enzymes are not destroyed by repeated incubation at 94 °C, the temperature at which all double stranded DNA denatures or melts to its two separate strands (155). 

Figure 4.3 Reversible Camot cycle, showing steps (1) reversible isothermal expansion at th (2) reversible adiabatic expansion and cooling from th to tc (3) reversible isothermal compression at tc (4) reversible adiabatic compression and heating back to the original starting point. The total area of the Camot cycle, P dV, is the net useful work w performed in the cyclic process (see text).

V). The centers resemble PSII of chloroplasts and have a high midpoint electrode potential E° of 0.46 V. The initial electron acceptor is the Mg2+-free bacteriopheophytin (see Fig. 23-20) whose midpoint potential is -0.7 V. Electrons flow from reduced bacteriopheophytin to menaquinone or ubiquinone or both via a cytochrome bct complex, similar to that of mitochondria, then back to the reaction center P870. This is primarily a cyclic process coupled to ATP synthesis. Needed reducing equivalents can be formed by ATP-driven reverse electron transport involving electrons removed from succinate. Similarly, the purple sulfur bacteria can use electrons from H2S. 

The principle of microscopic reversibility or detailed balance is used in thermodynamics to place limitations on the nature of transitions between different quantum or other states. It applies also to chemical and enzymatic reactions each chemical intermediate or conformation is considered as a state. The principle requires that the transitions between any two states take place with equal frequency in either direction at equilibrium.52 That is, the process A — B is exactly balanced by B — A, so equilibrium cannot be maintained by a cyclic process, with the reaction being A — B in one direction and B — > C — A in the opposite. A useful way of restating the principle for reaction kinetics is that the reaction pathway for the reverse of a reaction at equilibrium is the exact opposite of the pathway for the forward direction. In other words, the transition states for the forward and reverse reactions are identical. This also holds for (nonchain) reactions in the steady state, under a given set of reaction conditions.53... 

From the data presented in Chapter 10, it becomes evident that the extreme longevity of the artificial surfactant-stabilized microbubbles described therein is, in part, related to their continuous interaction with the simultaneously formed mixed micelle population in the saturated surfactant solution. More specifically, the surfactant-stabilized microbubbles produced by mechanical agitation of saturated solutions of either CAV-CON s Filmix 2 or Filmix 3 apparently undergo a cyclical (or reversible) process of microbubble formation/coalescence/fission/disappearance, where the end of each cycle is characterized by a collapse of the lipid-coated microbubbles into large micellar structures (i.e., rodlike multimolecular aggregates), only to re-emerge soon after as newly formed, lipid-coated microbubbles (see also below). 

We know from experience that any isolated system left to itself will change toward some final state that we call a state of equilibrium. We further know that this direction cannot be reversed without the use of some other system external to the original system. From all experience this characteristic of systems progressing toward an equilibrium state seems to be universal, and we call the process of such a change an irreversible process. In order to characterize an irreversible process further, we use one specific example and then discuss the general case. In doing so we always use a cyclic process. 

We then come to a general conclusion based on experience. No isolated system can be returned to its original state when a natural cyclic process takes place in the system. This statement may be considered as one statement of the Second Law of Thermodynamics. Although there is no rigorous proof of such a statement, all experience in thermodynamics attests to its validity. One concludes, then, that there must be some monotonically varying function that is related to this concept of reversibility. The value of this function for... 

In Section 3.3 we concluded that an isolated system can be returned to its original state only when all processes that take place within the system are reversible otherwise, in attempting a cyclic process, at least one work reservoir within the isolated system will have done work and some heat reservoir, also within the isolated system, will have absorbed a quantity of heat. We sought a monotonically varying function that describes these results. The reversible Carnot cycle was introduced to investigate the properties of reversible cycles, and the generality of the results has been shown in the preceding sections. We now introduce the entropy function. 

From these results, it is seen that the sorbents have excellent selectivities and olefin capacities. The isotherms are also relatively linear. The linearity is desirable for cyclic processes such as PSA (Rege, Padin, and Yang, 1998). Diffusion rates and isotherm reversibilities have also been measured on these systems, and they were all highly suitable for PSA. 

Equation (1.58) applies to any isothermal or adiabatic reversible cyclic processes. If there are many isothermal and adiabatic processes from high temperature TH to low temperature TL before the process goes back to its original state, any reversible cyclic process [Equation (1.58)] can be generalized as ... 

For an irreversible cyclic process, the summation of dq / T is less than 0, so the efficiency of an irreversible process is lower than that of a reversible one (Clausius) ... 

The solution of the puzzle is according to modern views that in the case of a cyclic process the only possible stationary value of the rotational flow in a cyclic sequence is zero, which is known as the principle (or axiom) of microscopic reversibility. 

Further insight may be gained by study of an arbitrary reversible cyclic process, as represented schematically on a PV diagram in Fig. 5.4. We divide the entire closed area by a series of reversible adiabatic curves since such curves cannot intersect (see Prob. 5.1), they may be drawn arbitrarily close to one another. A few of these curves are shown on the figure as long dashed lines. We connect adjacent adiabatic curves by two short reversible isotherms which approximate the curve of the general cycle as closely as possible. The approxima-... 

Thus the quantities dQrev/ T sum to zero for any series of reversible processes that causes a system to undergo a cyclic process. We therefore infer the existence of a property of the system whose differential changes are given by these quantities. The property is called entropy (en -tro-py) S, and its differential changes are... 

---