Reversible and irreversible processes

Reversible and irreversible processes. In discussing Berthelot s principle we were led to ask the question whether or not it is possible to deduce the direction of a chemical reaction from the magnitude or the sign of the heat evolution which accompanies it. In other words If a quantity of heat + 0 is set free in going from a state. 4 to a state B, will the change always take place from A to B, or, if not, under what conditions will it do so Or in general Under what conditions can we predict the direction in which any particular process will go  

We are therefore always trying to find new laws by means of which we may predict the occurrence of natural phenomena and the course which they will take. In the following we shall become acquainted with a law which, hke the law of the 

Besides the transfer of heat from places of higher to places of lower temperature, there are a number of other simple irreversible processes. The most important are  

All these irreversible processes take place spontaneously whenever occasion offers. A gas always flows into a vacuum when there is no obstruction to its flow. The electric current always produces heat in flowing through a resistance, and so on. 

If we could construct a machine which, after operating, would leave all its parts in their original condition, and which would Digitized by Microsoft  

If the flow of heat into or out of the system is to be reversible, what must be true of ST7 

Small increment of heat transferred from system to surroundings 

Suppose you have a system made up of water only, with the container and everything beyond being the surroundings. Consider a process in which the water is first evaporated and then condensed back into its original container. Is this two-step process necessarily reversible  

Let s next examine some aspects of reversible and irreversible processes, first with respect to the transfer of heat. When two objects at different temperatures are in contact, heat flows spontaneously from the hotter object to the colder one. Because it is impossible to make heat flow in the opposite direction, from colder object to hotter one, the flow of heat is an irreversible process. Given these facts, can we imagine any conditions under which heat transfer can be made reversible  

Throughout this study you will meet the term thermodynamical reversibility. The degree of reversibility of the electrode reaction can have a profound effect on the polarographic behaviour and influence its analytical application. However for the present purposes a simple qualitative picture is sufficient. 

Thermodynamical reversibility is not whether the reaction can run in reverse or not, but a question of energy and kinetics. 

Cadmium ions (in KCl) undergo a thermodynamically reversible reduction to cadmium metal. However a certain percentage of the cadmium metal atoms formed are continuously reoxidised back to cadmium ions. Both the forward and this back reaction are rapid. The rate of the overall reaction from cadmium ions to the metal is a balance of the forward and back reaction rates with the forward dominating. It is the back reaction which determines whether the electrode process is thermodynamically reversible. 

In a thermodynamically reversible electrode reaction the back reaction, from products back to the original species, occurs at an appreciable rate (at the potential of the wave) and must be taken into account. In a thermodynamically irreversible process the back reaction rate is negligible at the potential of the polarographic wave. In a reversible process the direction of the electrode reaction repeatedly reverses, for individual molecules or ions, between forward and back reactions. The overall reaction goes forward because the forward rate is the more rapid. An irreversible process is a one way only process and does not reverse at the potential of the wave. 

Since a thermodynamically reversible electrode process is one in which the the overall reaction rate is a balance between the forward reaction to the product and the back reaction from product back to the original species, both the original species and the products must control the properties of the wave and the potential at which the overall reaction occurs. Thus the half wave potential of the wave, is controlled by the energy difference between the original species and the electrode reaction product. The half wave potential will lie close to the theoretical standard electrode potential for the reaction. 

A process, which involves the spontaneous change of a system from a state to some other state, is called spontaneous or natural process. As such a process cannot be reversed without help of an external agency, the process is called an irreversible process. 

As a result of the irreversible or spontaneous process, the system has become degraded, i.e., energy which was available for doing useful work to the surroundings has become converted into thermal energy (heat) in which form it is no longer available for external purposes. 

The system will eventually arrive at a state in which the energy available for doing useful work to the surroundings is completely consumed. 

The equilibrium state is a state of rest. Once at equilibrium, a system will not move away from equilibrium unless some external agency (the surroundings) acts on it. A process during which the system is never away from equilibrium is called a reversible process. This statement is obviously contradictory to the definition of equilibrium. 

Therefore the reversible process is an imaginary one. However, if a process proceeds with an infinitesimally small driving force in such a way that the system is never more than an infinitesimal distance from equilibrium, a condition which is virtually indistinguishable from equilibrium, then the process can be regarded as a reversible process. Thus a reversible process is infinitely slow. 

For a simple reversible chemical reaction, if one path is preferred for the backward reaction, the same path must also be preferred for the reverse reaction. This is called the principle of microscopic reversibility. Time can be measured by reversible, periodic phenomena, such as the oscillations of a pendulum. However, the direction of time cannot be determined by such phenomena it is related to the unidirectional increase of entropy in all natural processes. Some ideal processes may be reversible and proceed in forward and backward directions. 

Entropy in an isolated system increases dS/dt 0 until it reaches equilibrium dS/dt = 0, and displays a direction of change leading to the thermodynamic arrow of time. The phenomenological approach favoring the retarded potential over the solution to the Maxwell field equation is called the time arrow of radiation. These two arrows of time lead to the Einstein-Ritz controversy Einstein believed that irreversibility is based on probability considerations, while Ritz believed that an initial condition and thus causality is the basis of irreversibility. Causality and probability may be two aspects of the same principle since the arrow of time has a global nature. 

The term irreversibility has two different uses and has been applied to different arrows of time. Although these arrows are not related, they seem to be connected to the intuitive notion of causality. Mostly, the word irreversibility refers to the direction of the time evolution of a system. Irreversibility is also used to describe noninvariance of the changes with respect to the nonlinear time reversal transformation. For changes that generate space-time symmetry transformations, irreversibility implies the impossibility to create a state that evolves backward in time. Therefore, irreversibility is time asymmetry due to a preferred direction of time evolution. 

This phenomenon is associated with the level of entropy production due to the irreversibility of the process. Entropy is not conserved it is the extensive parameter of heat. 

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 return to the piston-and-cylinder arrangement discussed in Section 2.3. In that discussion we did not completely describe the process because we were interested only in developing the concept of work. Here, to complete the description, we choose an isothermal process and a gas to be the fluid. We then have a gas confined in the piston-and-cylinder arrangement. A work reservoir is used to exert the external force, Fe, on the piston this reservoir can have work done on it by the expansion of the gas or it can do work by compressing the gas. A heat reservoir is used to make the process isothermal. The piston is considered as part of the surroundings, so the lower surface of the piston constitutes part of the boundary between the system and its surroundings. Thus, the piston, the cylinder, and the two reservoirs constitute the surroundings. 

The gas is compressed under the conditions that the work reservoir exerts the pressure Px on the piston. The work done on the gas and associated with the pressure of the gas is 

In the general case we consider any system that is capable of being used 

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 

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We adopt the nomenclature introduced by Hawthorne and Davis [1], in which compressor, heater, turbine and heat exchanger are denoted by C, H, T and X, respectively, and subscripts R and I indicate internally reversible and irreversible processes. For the open cycle, the heater is replaced by a burner, B. Thus, for example, [CBTX]i indicates an open irreversible regenerative cycle. Later in this book, we shall in addition, use subscripts... 

The importance of these four equations cannot be overemphasized. They are total differentials for U as f(S, V), H as /(S./ ), A as f V,T), and G as j p,T). Although they were derived assuming a reversible process, as total differentials they apply to both reversible and irreversible processes. They are the starting points for the derivation of general differential expressions in which we express U, H, A and Casa function of p, V, T, Cp and Ci. a These are the relationships that we will now derive. 

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. 

Table 20.3 lists the reversible and irreversible processes that may be significant in the deep-well environment.3 The characteristics of the specific wastes and the environmental factors present in a well strongly influence which processes will occur and whether they will be irreversible. Irreversible reactions are particularly important. Waste rendered nontoxic through irreversible reactions may be considered permanently transformed into a nonhazardous state. A systematic discussion of mathematical modeling of groundwater chemical transport by reaction type is provided by Rubin.30... 

The relationships between the components of the Hantzsch triangle were considered in-depth in the monograph 2 and references therein. Although the problem of reactivity of ambident substrates has been studied over many years and from different points of view, the complexity of the starting system and its numerous reaction pathways do not allow one to reliably predict the results of O-alkylation in each particular case, because it is necessary to take into account the rates of numerous reversible and irreversible processes as well as the thermodynamic factors responsible for the position of the equilibrium it is necessary to take solvent effects into consideration when estimating the thermodynamic factors. All accumulated observations are approximated by several empirical mles included in monographs 2 and 3. 

Influence of Mass Transport on Charge Transfer. Electrochemically Reversible and Irreversible Processes... 

For a scientist, the primary interest in thermodynamics is in predicting the spontaneous direction of natural processes, chemical or physical, in which by spontaneous we mean those changes that occur irreversibly in the absence of restraining forces—for example, the free expansion of a gas or the vaporization of a hquid above its boiling point. The first law of thermodynamics, which is useful in keeping account of heat and energy balances, makes no distinction between reversible and irreversible processes and makes no statement about the natural direction of a chemical or physical transformation. 

The entropy, Spontaneous vs non-spontaneous, Reversible and irreversible processes, Calculation of entropy changes (Isothermal, isobaric, isochoric, adiabatic), Phase changes at equilibrium, Trouton s rule, Calculation for irreversible processes... 

We conclude by summarizing in Table 3.1 some key distinctions between reversible and irreversible processes, taking as an example the expansion of a gas against a piston, with external pressure Fext ... 

THOMSON PRINCIPLE. The hypothesis that, if thermodynamically reversible and irreversible processes take place simultaneously in a system, the laws of thermodynamics may be applied to the reversible process while ignoring for this purpose the creation of entropy due to die irreversible process. Applied originally by Thomson to the case of... 

The hepatic disposition parameters of a drag, representing reversible and irreversible processes, are calculated using the following equations ... 

Since both reversible and irreversible processes are influenced in distinct ways by temperature and water activity, the first step of a humid aging study consists of searching for the conditions (T, RH, sample thickness) in which both phenomena can be clearly decoupled, as in Figs 14. lc and d. The interpretation of experimental results and the modeling of the kinetics of property changes would be difficult or even impossible if physical characteristics such as ar d (or better D) were not known. 

As shown in Chap. 2, attaining analytical explicit solutions is considerably more complex for nonplanar geometries. This section studies quasi-reversible and irreversible processes when a potential step is applied to a spherical electrode, since this solution will be very useful for discussing the behavior of these electrode reactions when steady-state conditions are addressed in the next section. Moreover, the treatment of other electrode geometries seldom leads to explicit analytical solutions and it is necessary in most cases to use numerical treatments. 

In the development of the second law and the definition of the entropy function, we use the phenomenological approach as we did for the first law. First, the concept of reversible and irreversible processes is developed. The Carnot cycle is used as an example of a reversible heat engine, and the results obtained from the study of the Carnot cycle are generalized and shown to be the same for all reversible heat engines. The relations obtained permit the definition of a thermodynamic temperature scale. Finally, the entropy function is defined and its properties are discussed. 

Having defined the entropy function, we must next determine some of its properties, particularly its change in reversible and irreversible processes taking place in isolated systems. (In each case a simple process is considered first, then a generalization.)... 

Experimental errors molar absorption coefficients, +/-5% luminescence quantum yield, +/—10%, luminescence lifetime, +/-5% redox potentials, 10 mV and 20 mV for reversible and irreversible processes, respectively. 

The distinction between reversible and irreversible processes is illustrated by the following example. Example 1... 

Note that the total heat is the same for both reversible and irreversible processes. 

Equation (5.14) can be written for both the reversible and irreversible processes ... 

Since the heat supplied, Aq at constant pressure, P is equal to the change in enthalpy, AH, which is itself a state function - and is therefore identical for both reversible and irreversible processes - hence we can write ... 

If (Ep - Ei/2 is eliminated between the equations expressing peak potentials for reversible and irreversible processes (73) % one finds ... 

Commentary Not all conceivable processes to which a system could in principle be subjected can actually be realized we shall encounter such cases later. Operationally, the distinction between reversible and irreversible processes introduces an element of patience. Only if one waits a long time between successive steps that involve just infinitesimal alterations in the system can one hope to produce reversible changes. Clearly, all dissipative effects such as friction must be avoided also. 

It should be clear that AS corresponds to an entropy change, that nf and n, simulate firreversible processes, and that contour lines on a map are analogous to tabulations of entropy values. The shortcomings of the parable should be explored by the reader. 

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