Process quasi-static

In the limit of very slow change (quasi-static process) the frictional component is zero and then the work done by the external force equals the free energy change, i.e.. 

This phenomena has been attributed to the very high strain rates associated with shock loading and the subsonic restriction on dislocation velocity requiring the generation and storage of a larger dislocation density during the shock process than for quasi-static processes [1], [2], [12],... 

If the grains of sand are small, each step does not represent a very large departure from equilibrium between p and ptxt. This process is an example of a quasi-static process that is, one in which the process is never far from equilibrium during the expansion. 

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. 

If there are no dissipative effects, that is, friction, viscosity, inelasticity, electrical resistance, and so on, during a quasi-static process, the process is termed reversible. Only an infinitesimal change is required to reverse the process, a concept that leads to the name reversible. Most industrial processes exhibit heat transfer over finite temperature differenees, mixing of dissimilar substances, sudden changes in phase, mass transport under finite concentration differences, free expansion, pipe friction, and other mechanical, chemical, and thermal nonidealities, and consequently are deemed irreversible. An irreversible process always involves a degradation of the potential of the process to do work, that is, will not produce the maximum amount of work that would be possible via a reversible process (if such a process could occur). 

The excess heat AW is the additional work in a non-quasi-static process. It is given as the difference between work in a non-quasi-static process and work in the quasi-static process ... 

We consider the work in a quasi-static (QS) process and define an adiabatic invariant. In the quasi-static process, we assume that the probability density is given as p(x, t) = pme(x, c(tj). Then,... 

A reversible change means an idealized, quasi-static process performed by infinitesimal modifications of a... 

The way of reasoning we have used here comprises, according to the energetics of Bronsted, a coupling of two basic processes, viz., the mechanical process of increasing the interfacial area and the transport of substances to the surface phase. A quasi-static process is always made up of coupled basic processes.)... 

We consider an arbitrary adiabatically isolated system consisting of two parts in thermal contact. The system is at a uniform temperature t, and we assume that the equilibrium states of each of the parts can be characterized by t and one other parameter. Thus, for a quasi-static process,... 

Figure 1.4 Comparison of changes of state as represented on a state (PV) diagram for a pure, one-phase substance. During an (a) irreversible process, intermediate states are unknown and unknowable during a (b) quasi-static process, the system moves in small discrete steps between identifiable equilibrium states during a (c) reversible change, every intermediate state is a well-defined equilibrium state.

Even though a quasi-static process is driven differentially, the driving forces may still contain dissipative components. These components may arise because some properties have finite differences across boundaries or they may arise from differential effects accumulated over a finite process. If we could remove all dissipative components so the process would be driven only by conservative forces, then the change of state would be reversible. This reversible limit can be expressed as... 

Figure 1.5 Schematic of a quasi-static process compared with a finite irreversible process. The system initially in a state having properties T,-, P,-, and N, is to be changed to a final state having Ty, Pjr, and Ny. In the finite irreversible process (fop) the system passes through intermediate states that are undefined. During the quasi-static process (bottom) the change occurs in differential stages at the end of each stage the system is allowed to relax to an intermediate state that is well-defined. In both processes, overall changes in state functions, such as AT = Ty - T, and AP =...

Equations (2.1.12) and (2.1.13) are written for finite irreversible processes. For a quasi-static process, the dissipative pressure is a differential quantity d9. Moreover, for a reversible change, dissipative components vanish 9 = 0), and P = Pg f. Then (2.1.9) gives the reversible work. 

How does the work for an irreversible process differ from that for a quasi-static process and for a reversible change ... 

The quasi-static process is an idealization that allows us to associate a path drawn on the thermodynamic plane with an actual process. It is a mental device that we use to draw connections between mathematical operations on the thermodynamic plane and real processes that can be conducted experimentally. Since this is a mental exercise, we are not concerned as to whether this is a practical way to run the process. In fact, this is a rather impractical way of doing things Gradients are desirable because they increase the rate of a process and decrease the time it takes to perform the task. This does not mean that the quasi-static concept is irrelevant in real life. When mathematics calls for an infinitesimal change, nature is satisfied with a change that is small enough. If an actual process is conducted in a way that does not upset the equilibrium state too much, it can then be treated as a quasi-static process. 

Strictly speaking, thermodynamics applies to systems in equilibrium. When we refer to the pressure and temperature of a system we imply that the system is in equilibrium so that it is characterized by a single (uniform) value of pressure and temperature. Thermodynamics also applies rigorously to quasi-static processes, which allow the system to maintain a state of almost undisturbed equilibrium throughout the entire process. 

This relationship fully describes all of the stable equilibrium states of a simple system with n components. However, there is no single fundamental equation governing the properties of all materials. The fundamental equation is represented by a surface in (3 + n) dimensional space. Quasi-static processes can be represented by a curve on this surface. The points on this surface represent stable equilibrium states of this simple system. For the entropy and internal energy, the canonical variables consist of extensive parameters. For a simple system, the extensive properties are S, U, and V, and the fundamental equations define a fundamental surface of entropy S = S U,V) in the Gibbs space of S, U, and V. 

In the following discussions, it will be usefiil to introduce the term quasi-static. This term has various meanings as used by various authors, but in this chapter it refers to an irreversible process carried out in a very large number of very small steps. The difference between a quasi-static and a reversible process is that the reversible process refers to a series of stable equilibrium states, while the quasi-static process is a series of metastable equilibrium states. After every step of a reversible process, the system is at stable equilibrium with only two constraints. After every step of a quasi-static process, the system is at a metastable equilibrium and has at least three constraints. This concept and the need for it will become clear by considering some examples. 

Let us consider an open thermodynamic system consisting of v components, i.e. containing particles of u kinds. I he first and second principles of thermodynamics written together for a quasi-static process in such a system represent the Gibbs fundamental equation in its energetic expression ... 

Consider a part P of the system surrounded by an adiabatic wall where a small change is caused by work applied from the environment (Figure 2.3). The minimum work 5 WVin to cause this change is that of a quasi-static process. It is given by... 

For slow velocities of compression or dilation of the gas, so-called quasi-static processes, dA is given as... 

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