Reversible processes defined

Why in the world would we be interested in such a strange kind of impossible process It s simple, really. The reason the reversible process (defined as a continuous succession of equilibrium states) is important in the thermodynamic model is that it is the only kind of process that our mathematical tools of differentiation and integration can be applied to - they only work on continuous functions. Once our crystal of diamond leaves its state of equilibrium at 25 °C, practically anything could happen to it, but as long as it settles back to equilibrium at 50 °C, all of its state variables have changed by fixed amounts from their values at 25 °C. We have equations to calculate these energy differences, but they refer to lines and surfaces in our model, and that means that they must refer to continuous equilibrium between the two states. 

The concept described above will now be elaborated upon by examining the effect of expansion for a reversible process. Defining H = U + PV, where U refers to internal energy, T to temperature and P to pressure, and substituting it in Eq. (1) results in ... 

Since is defined as work done on the system, the minimum amount of work necessary to produce a given change in the system is that in a reversible process. Conversely, the amount of work done by the system on the surroundings is maximal when the process is reversible. 

In analogy to the constant-pressure process, constant temperature is defined as meaning that the temperature T of the surroundings remains constant and equal to that of the system in its initial and final (equilibrium) states. First to be considered are constant-temperature constant-volume processes (again Aw = 0). For a reversible process... 

The second law of thermodynamics was actually postulated by Carnot prior to the development of the first law. The original statements made concerning the second law were negative—they said what would not happen. The second law states that heat will not flow, in itself, from cold to hot. While no mathematical relationships come directly from the second law, a set of equations can be developed by adding a few assumptions for use in compressor analysis. For a reversible process, entropy, s, can be defined in differential form as... 

The process is assumed reversible. This defines entropy as constant and therefore ds = 0, making Tds = 0. The enthalpy equation is simplified to... 

There are several general classes of pericyclic reactions for which orbital symmetry factors determine both the stereochemistry and relative reactivity. The first class that we will consider are electrocyclic reactions. An electrocyclic reaction is defined as the formation of a single bond between the ends of a linear conjugated system of n electrons and the reverse process. An example is the thermal ring opening of cyclobutenes to butadienes ... 

The second law of thermodynamics also consists of two parts. The first part is used to define a new thermodynamic variable called entropy, denoted by S. Entropy is the measure of a system s energy that is unavailable for work.The first part of the second law says that if a reversible process i f takes place in a system, then the entropy change of the system can be found by adding up the heat added to the system divided by the absolute temperature of the system when each small amount of heat is added ... 

In earlier days, A was called the work function because it equals the work performed on or by a system in a reversible process conducted at constant temperature. In the next chapter we will quantitatively define work, describe the reversible process and prove this equality. The name free energy for A results from this equality. That is, A A is the energy free or available to do work. Work is not a state function and depends upon the path and hence, is often not easy to calculate. Under the conditions of reversibility and constant temperature, however, calculation of A A provides a useful procedure for calculating u ... 

Entropy can be described by considering a closed system undergoing a reversible process. The entropy change, dS, of the system is defined by the relationship... 

Although from the thermodynamic point of view one can speak only about the reversibility of a process (cf. Section 3.1.4), in electrochemistry the term reversible electrode has come to stay. By this term we understand an electrode at which the equilibrium of a given reversible process is established with a rate satisfying the requirements of a given application. If equilibrium is established slowly between the metal and the solution, or is not established at all in the given time period, the electrode will in practice not attain a defined potential and cannot be used to measure individual thermodynamic quantities such as the reaction affinity, ion activity in solution, etc. A special case that is encountered most often is that of electrodes exhibiting a mixed potential, where the measured potential depends on the kinetics of several electrode reactions (see Section 5.8.4). 

Woodward and Hoffmann define as electrocyclic reactions the formation of a single bond between the termini of a system containing k n electrons, and the reverse process(89) ... 

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... 

Entropy is the ratio of a body s energy to its temperature according to the Clausius equality (as defined in the next section). For a reversible process, the change in entropy is defined by... 

Soon after it was shown that ubiquitin is conjugated to proteins, it was determined that this was a reversible process and deubiquitinating enzymes, or DUBs, could remove ubiquitin from ubiquitinated proteins [18, 19]. As the genes for ubiquitin and ubiquitin-like proteins were identified it became clear that all ubiquitin family members were synthesized as proproteins and processed to reveal the C-terminal glycylglycine of the active proteins [20]. Based on this information, DUBs were defined as proteases that cleave at the C-terminus of ubiquitin or ubiquitin-like proteins to reverse conjugation to target proteins and also process the proproteins. 

Any finite expansion that occurs in a finite time is irreversible. A reversible expansion can be approximated as closely as desired, and the values of the thermodynamic changes can be calculated for the limiting case of a reversible process. In the limiting case, the process must be carried out infinitely slowly so that the pressure P is always a well-defined quantity. A reversible process is a succession of states, each of which is an equilibrium state, in which the temperature and pressure have well-defined values such a process is also called a quasi-static process. 

Melting point The melting point of a substance is defined as the temperature at which a solid substance undergoes a phase change to a liquid. The reverse process, the temperature at which a hquid freezes to a solid, is called the freezing point. For a given substance, the melting point is identical to... 

In thermodynamics, entropy change is defined in a reversible process as... 

Fig 6 The Rankine-Hugoniot curve defines states that can be induced in substance by shock compression in terms of pressure (p), specific volume (V), and internal energy (E). Shock compression from initial state B to shocked state C follows the R-H curve and dissipates energy shown by the hatched area. Thus shock compression is not a reversible process—unlike adiabatic compression, which is, at least ideally reversible... 

Consider an uncharged metal and an electron just outside the metal.31 The change of energy at a given temperature and pressure when the electron moves from the point just outside to the point inside the metal defines the binding energy of the electron to the material.32 Consider now the reverse process, that is, when the electron... 

This is a fundamental equation of physical chemistry because it enables us to assign a physical significance to G as defined by Equation (12). Equation (14) shows that for a constant temperature, constant pressure, and reversible process... 

On the return sweep, the reduction continues since the surface C0/Cn still favors the formation of R until the balance shifts at 2 rev and oxidation current is observed for the remainder of the sweep. Other than the fact that the base line for the reverse wave is less well-defined, the shapes of the waves are very nearly the same in both directions for the reversible process. 

A detailed electrochemical study on 16 different Cu(R2Dtc)2 complexes has been reported (313). The oxidation of the Cu(R2Dtc)2 complexes is unambiguously defined as the one-electron reversible process shown by Eq. 3. 

First of all, we define the transition rates for our stochastic model using an ansatz of Kawasaki [39, 40]. In the following we use the abbreviation X for an initial state (07 for mono- and oion for bimolecular steps), Y for a final state (ct[ for mono- and a[a n for bimolecular steps) and Z for the states of the neighbourhood ( cr f 1 for mono- and a -1 a -1 for bimolecular steps). If we study the system in which the neighbourhood is fixed we observe a relaxation process in a very small area. We introduce the normalized probability W(X) and the corresponding rates 8.(X —tY Z). For this (reversible) process we write down the following Markovian master equation... 

For the reversible processes we can define the ratio of the transition rates using equation (9.2.30) ... 

We have defined a spontaneous process as one that proceeds on its own without any external influence (Section 8.13). The reverse of a spontaneous process is always nonspontaneous and takes place only in the presence of some continuous external influence. Consider, for example, the expansion of a gas into a vacuum. When the stopcock in the apparatus shown in Figure 17.1 is opened, the gas in bulb A expands spontaneously into the evacuated bulb B until the gas pressure in the two bulbs is the same. The reverse process, migration of all the gas molecules into one bulb, does not occur spontaneously. To compress a gas from a larger to a smaller volume, we would have to push on the gas with a piston. 

PI 1.1 The first of the four fundamental equations of Gibbs equation (11.10) is obtained by combining equation (11.6), the statement of the First Law applied to the system, with equation (11.7), the Second Law statement for a reversible process, again applied to the system, and equation (11.8) that calculates reversible pressure-volume work. Start with equation (11.10) and the defining equations for H, A, and G equations (11.1), (11.2), and (11.3), and derive the other Gibbs equations equations (11.11), (11.12), and (11.13). ... 

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