The Reverse Cycle

If we designate the heat and work quantities for the reverse cycle by primed symbols, the reverse and forward relationships are 

e is the same for both the forward and the reverse cycles.  

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The important point here is that the efficiency is a function of the temperature ratio 6 as well as the pressure ratio r (and d, whereas it is a function of pressure ratio only for the reversible cycle, [CHT]r. 

One of these alternate models, postulated by Gunter Wachtershanser, involves an archaic version of the TCA cycle running in the reverse (reductive) direction. Reversal of the TCA cycle results in assimilation of CO9 and fixation of carbon as shown. For each turn of the reversed cycle, two carbons are fixed in the formation of isocitrate and two more are fixed in the reductive transformation of acetyl-CoA to oxaloacetate. Thus, for every succinate that enters the reversed cycle, two succinates are returned, making the cycle highly antocatalytic. Because TCA cycle intermediates are involved in many biosynthetic pathways (see Section 20.13), a reversed TCA cycle would be a bountiful and broad source of metabolic substrates. 

It is important to select stoichiometric co-reductants or co-oxidants for the reversible cycle of a catalyst. A metallic co-reductant is ultimately converted to the corresponding metal salt in a higher oxidation state, which may work as a Lewis acid. Taking these interactions into account, the requisite catalytic system can be attained through multi-component interactions. Stereoselectivity should also be controlled, from synthetic points of view. The stereoselective and/or stereospecific transformations depend on the intermediary structure. The potential interaction and structural control permit efficient and selective methods in synthetic radical reactions. This chapter describes the construction of the catalytic system for one-electron reduction reactions represented by the pinacol coupling reaction. 

A clue to the direction that needs to be followed to reach a criterion of spontaneity can be obtained by noticing in Table 5.1 that Q and Ware equal to zero for the reversible cycle but are not zero for the irreversible cycle. In other words, it is changes in the surroundings as well as changes in the system that must be considered in distinguishing a reversible from an irreversible transformation. Evidently, then, we need to find a... 

Thus, the amount of heat returned to the high-temperature reservoir in the reverse cycle is greater than the amount removed from it in the forward cycle. 

For 6 to be a generally useful function we must remove any specifications as to the namre of the reversible cycle through which the substance is being carried. Let us represent a general reversible cycle by the example illustrated in Figure 6.5(a). This cycle also can be approximated in Carnot cycles, as illustrated in... 

The Carnot cycle is of historical importance. The reversible cycle was introduced by a French engineer N.S. Carnot in 1824 and led to the development of the second law of thermodynamics. The importance of the Carnot cycle is that it sets up a standard thermal cycle performance for the actual cycles to compare with. 

It is important to also consider the reverse cycle of the reaction shown in Eq. (9-2). This reverse cycle can generate H2 with a very low activation energy. We describe this reverse cycle in detail, presenting the structures, electron states and energy diagrams of the complexes and transition states in the reaction of Eq. (9-2) in the next section, Section 2.2.3. 

Show that the reverse cycle time for the catalytic cycle illustrated in Figure 4.2B is given by rc cle = E0/J for this mechanism. 

A common feature of all single-cycle kinetics discussed so far is a one-plus rate behavior with reaction order between zero and one with respect to the reactant, A (and for a possible reverse rate, with respect to the product, P). The Michaelis-Menten and Briggs-Haldane rate equations 8.18 and 8.22 have the same algebraic form, and so has the initial rate in the reversible cycle, that is, eqn 8.24 with terms involving CP still being insignificant. This common one-plus form can be rearranged ... 

Hence all periodic reversible heat engines working between the same two temperatures must convert the same fraction of the heat absorbed at the higher temperature into work. The maximum efficiency of a heat engine therefore depends only on the temperatures between which it works. In order to calculate this function of the temperature it is sufficient to determine the work done in an arbitrary reversible cycle, which we may perform with any arbitrarily chosen working substance. For simplicity we shall choose a perfect gas as working substance, as its equation of condition is accurately known. The reversible cycle which we shall suppose it to perform is known as CamoFs cycle. It is as follows ... 

The sum of the quantities of heat absorbed in the reversible cycle, each divided by the absolute temperature at which the absorption took place, is zero. 

If portions of the cycle are irreversible, if, for example, part of the heat absorbed at reaches Tg by radiation or conduction, the efficiency will be less than that of the reversible cycle. Thus, using the new convention as to the sign of Q, we have... 

Let us connect them together to a combined heat cycle OO in such a way that the mirror (the reverse cycle O ) is gaining the message about the structure of the direct cycle O. This message is (carrying) the information H (X I Y) about the structure of the transformation (transfer) process (O= tC) being observed. The mirror O s K is gaining this information H (X I Y) on its noise input H(Y I X ) [while H(X )=H(Y) is its input entropy]. 

If any two points A and B are chosen along the reversible cycle, the cycle may be broken into two reversible paths 1 and 2. The closed cycle integral may be written as the sum of two integrals ... 

The reaction is basically the citric acid cycle run in reverse. Where the Krebs cycle takes complex carbon molecules in the form of sugars and oxidizes them to C02 and water, the reverse cycle takes C02 and water to make carbon compounds. This process is used by some bacteria to synthesize carbon compounds, sometimes using hydrogen or sulfates as electron donors. The reaction is a possible candidate for prebiotic early Earth conditions and so it is of interest in the origin of life. On the early Earth, a primitive form of acetyl-CoA-like thioacetate played the role of the essential coenzyme. It has been found that some of the steps can be catalyzed by minerals. Thus, the FeS world proposes that the reverse citric acid cycle operated nonenzymatically on the primitive Earth. The question is whether it is possible to retrace other ancient metabolic pathways. Combination of the recently found plugged... 

Carnot s cycle has been thus far discussed for an ideal gas. Similar reversible cycles can be performed on other materials, including solids and liquids, and the efficiency of these cycles determined. The importance of the reversible cycle for the ideal gas is that, as has just been seen, it gives us an extremely simple expression for the efficiency, namely (T, Tc)/Th. Similarly, a theorem of Carnot shows that the efficiency of all reversible cyclj S,.Qperating.betwe.en, t % is the same, namely... 

For any engine we have only the possibilities expressed by (8.39). We have shown that the equality holds f or the reversible engine. Since the heat and work effects associated with an irreversible cycle are different from those associated with a reversible cycle, this implies that the value of j 4QIT for an irreversible cycle is different from the value, zero, associated with the reversible cycle. We have shown that for any engine the value cannot be greater than zero consequently, it must be less than zero. Therefore for irreversible cycles we must have... 

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