Reversible changes in state

For a reversible change in state of a closed system of constant composition, whereby the only work per-... 

Carnot cycle consists of four reversible steps, and therefore is a reversible cycle. A system is subjected consecutively to the reversible changes in state ... 

The first two of these equations relate to changes in state at constant entropy, that is, adiabatic, reversible changes in state. The derivative (dT/dV)s represents the rate of change of temperature with volume in a reversible adiabatic transformation. We shall not be much concerned with Eqs. (10.23) and (10.24). 

Equation (A2.1.15) involves only state fiinctions, so it applies to any infinitesimal change in state whether the actual process is reversible or not (although, as equation (A2.1.14) suggests, dS is not experimentally accessible unless some reversible path exists). 

In general the conditions under which a change in state of a gas takes place are neither isothermal nor adiabatic and the relation between pressure and volume is approximately of the form Pvk = constant for a reversible process, where k is a numerical quantity whose value depends on the heat transfer between the gas and its surroundings, k usually lies between 1 and y though it may, under certain circumstances, lie outside these limits it will have the same value for a reversible compression as for a reversible expansion under similar conditions. Under these conditions therefore, equation 2.70 becomes ... 

A quite different approach came from Chance and others using heme enzymes (1947). Purified horseradish peroxidase has a characteristic absorption spectrum which was visibly altered in the presence of hydrogen peroxide. When an appropriate substrate was added it was oxidized by the hydrogen peroxide and the spectrum reverted to that of the original state of the enzyme. Similar studies were performed with catalase, showing that prosthetic groups in enzymes underwent reversible changes in the course of their reactions. 

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... 

The heat absorbed by the surrounding reservoir during the irreversible reaction is 285,830 J, and this heat produces the same change in state of the reservoir as the absorption of an equal amount of heat supplied reversibly. If the surrounding reservoir is large enough to keep the temperature essentially constant, its entropy change is... 

We can obtain an explicit equation for the entropy of an ideal gas from the mathematical statements of the two laws of thermodynamics. It is convenient to derive this equation for reversible changes in the gas. However, the final result will be perfectly general because entropy is a state function. 

Picosecond Raman measurements have led to the proposal of a dynamic polarization model." In this model, 5i tS undergoes reversible changes in vibrational frequencies that are induced by solvent fluctuations. The mixing of a perturbing state with interconverts carbon-carbon double bonds with single bonds that leads S tS near the vertical geometry to proceed along the pathway for isomerization. 

Metal Ion Catalysis Metals, whether tightly bound to the enzyme or taken up from solution along with the substrate, can participate in catalysis in several ways. Ionic interactions between an enzyme-bound metal and a substrate can help orient the substrate for reaction or stabilize charged reaction transition states. This use of weak bonding interactions between metal and substrate is similar to some of the uses of enzyme-substrate binding energy described earlier. Metals can also mediate oxidation-reduction reactions by reversible changes in the metal ion s oxidation state. Nearly a third of all known enzymes require one or more metal ions for catalytic activity. 

The ability of copper ions to undergo reversible changes in oxidation state permits them to function in a variety of oxidation-reduction processes. Like iron, copper also provides sites for reaction with 02, with superoxide radicals, and with nitrite ions. 

These are hemoproteins that catalyze electron transfer through the reversible change in oxidation state of the heme iron.637 They are involved in the respiratory chain, and in a wide range of other processes such as photosynthesis and the nitrogen cycle. Over 50 cytochromes have been studied, notably cytochrome c, which is one of the best studied biological molecules. Bacteria in particular produce a wide range of cytochromes which currently are attracting much attention. 

Equation 6.33 provides the definition of exergy if state 1 is chosen as the state at ambient condition, namely, P, = P0 and = T0 the minimum amount of work required to transfer the system from environmental conditions to those at P2 and T2. At these conditions, this is the maximum amount of work available for the reverse process. That is the valuable idea behind the exergy concept to be able to assign to any process stream a value, its exergy, that expresses the confined work available in the stream. For the general change in state from P0r T0 to P, T, we can write the net energy input as... 

In a chiral photochromic system (Figure 1), A and B represent two different chiral forms of a bistable molecule, and a reversible change in chirality occurs upon light irradiation. The left-handed (S or M) and right-handed (R or P) forms of a chiral compound 91 represent two distinct states in a molecular binary logic element. 

When chain segments can move relatively freely in cured polymers, it is most likely due to low crosslink density or the mobility of the molecular chain structure. The glass transition temperature is a measure of the mobility of the molecular chains in the polymer network as a function of temperature. The glass transition is the reversible change in a polymer from (or to) a rubbery condition to (or from) a hard and relatively glassy state condition (Fig. 3.14). This transition occurs at a temperature called the glass transition temperature or Tg. It is... 

The equations developed in this section have been derived for mechanically reversible nonflow processes involving ideal gases. However, those equations which relate state functions only are valid for ideal gases regardless of the process and apply equally to reversible and irreversible flow and nonflow processes, because changes in state functions depend only on the initial and Anal states of the system. On the other hand, an equation for Q or W is specific to the case considered in its derivation. 

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