Reversible system general definition

There is a more general definition of reversibility which extends nicely to higher-order systems. Consider any mapping 7 (x) of the phase space to itself that satisfies In other words, if the map-... 

The word "catalysis" was first used by Berzelius in 1836 to describe a number of experimental observations, including Thenard s discovery in 1813 that ammonia is decomposed by metals. The most general definition of a catalyst states that "it is a substance which modifies the rate at which a chemical system attains equilibrium, without itself undergoing a chemical change". It follows that a catalyst can only accelerate a thermodynamically feasible reaction and cannot displace the position of the equilibrium in the case of a reversible reaction because the forward and the reverse reactions are accelerated to the same extent. 

The distinction between reversible and irreversible work is one of the most important in thermodynamics. We shall first illustrate this distinction by means of a specific numerical example, in which a specified system undergoes a certain change of state by three distinct paths approaching the idealized reversible limit. Later, we introduce a formal definition for reversible work that summarizes and generalizes what has been learned from the path dependence in the three cases. In each case, we shall evaluate the integrated work w 2 from the basic path integral,... 

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... 

Due to their high molecular mass (and other reasons), the vast majority of mAbs that have been approved or are currently in clinical development are administered by intravenous (IV) infusion. This route allows the total dose to be available in the circulation, as F (the systemically available fraction of the dose) is, by definition, 1. In consequence, maximum concentrations in serum are rapidly observed, and are higher compared to those achieved by other routes. Therefore, adverse reactions after IV administration occur more often but are generally reversible. In addition, IV infusions represent the most inconvenient (they often require hospitalization) as well as time- and cost-consuming means of administration. Consequently, ex-travascular routes have been chosen as alternatives, including subcutaneous administration (SC e. g., adalimumab, efalizumab) and intramuscular administration (IM e.g., palivizumab) (Table 3.4). 

Although, in general, transports are not reversible, we can idealize them as being reversible from the point of view of the system. This is because, by definition, we are not interested in the details of the processes that occur in the surroundings. Thus, we can imagine heat transfer to occur from a heat reservoir, which is constructed of a material with infinite heat conductivity, so that it maintains a uniform temperature as heat is withdrawn from it. Moreover, the reservoir is in contact with the boundary of the system sufficiently long so that the boundary is at the temperature of the reservoir. In this case, the decrease of the entropy of the reservoir is exactly equal to the entropy transported to the system ... 

In a photochromie system all of the refractive-index change is a result of photoinduced reactions of isolated molecules, and there is no mass transport over distances larger than molecular dimensions. Since each molecule functions independently, the spatial frequency response of photochromic systems extends from zero to the diffraction limit of the recording light. (This is frequently referred to as "molecular resolution.") While our definition of a photochromic system does not require that the process be reversible, many photochromic systems are reversible, optically and/or thermally (31). In fact, it is in general only with photochromic processes that one can obtain, reversible image recording. 

Oxidation-Reduction Indicators.—A reversible oxidation-reduction indicator is a substance or, more correctly, an oxidation-reduction system, exhibiting different colors in the oxidized and reduced states, generally colored and colorless, respectively. Mixtures of the two states in different proportions, and hence corresponding to different oxidation-reduction potentials, will have different colors, or depths of color every color thus corresponds to a definite potential which depends on the standard potential of the system, and frequently on the hydrogen ion concentration of the solution. If a small amount of an indicator is placed in another oxidation-reduction system, the former, acting as a potential mediator, will come to an equilibrium in which its oxidation-reduction potential is the same as that of the system under examination. The potential of the given indicator can be estimated from its color in the solution, and hence the potential of the system under examination will have the same value. 

A thermodynamically reversible half-reaction can be defined as one that can be made to proceed in either of two opposing directions by an infinitesimal shift in the potential from its equilibrium value. Contrary to general opinion, such reactions are rare. This definition should not necessarily be used as a basis for an experimental test for two reasons (i) a finite potential shift must be made to produce a finite net current, and (2) the point of zero current is not always the equilibrium potential. While irreversibility can be revealed in many systems, proof of thermodynamic reversibility at the molecular level in others is virtually impossible. 

Attention may be drawn to the fact that although certain restrictions were mentioned in the course of the foregoing deductions, the final results are of general applicability. The Gibbs-Helmholtz equations (25.31), (25.32) and (25.33), for example, will hold for any change in a closed system, irrespective of whether it is carried out reversibly or not. This is because the values of AF and AH (or AA and AH) are quite definite for a given change, and do not depend upon the path followed. The only condition that need be applied is the obvious one that the system must be in thermodynamic equilibrium in the initial and final states of the process, for only in these circumstances can the various thermodynamic functions have definite values ( 4d). 

Because the concept of entropy is generally not familiar to hydrologists, a brief introduction is probably in order. A thorough and rigorous explanation can be obtained from standard works such as those by Fast (I), Fitts (2), Katchalsky and Curran (3), Klotz (4), Lewis and Randall (5), and Prigogine (6). A statement of the second law of thermodynamics is generally used as a definition of entropy of a system as follows dS DQ/T, where dS is an infinitesimal change in entropy for an infinitesimal part of a process carried out reversibly, DQ is the heat absorbed, and T is the absolute temperature at which the heat is absorbed. In one sense, entropy is a mathematical function for the term... 

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