Quasistatic processes

Generai principies, representative appiications, fluctuations and irreversibie thermodynamics. Chapter 4 discusses quasistatic processes, reversibie work and heat sources, and thermodynamic engines. 

The purpose of this section is to show how the previous theory can be applied in practical calculations. For the time being only quasistatic processes have been... 

The purpose of this section is to show how the above theory can be applied in practical calculations. For the time being, only quasistatic processes have been studied in detail the subsequent discussion will thus focus on this limit. Two sorts of quantities enter into the theory the atom-atom distribution functions r) in a given electronic state j and the corresponding populations nj t). The total atom-atom distribution function gnv(r, t) is then... 

The force exerted by the substance within the cylinder on the lower force of the piston under these conditions is the product of the pressure exerted by the substance on the surface of the piston and the area of the piston. Moreover, the product of the area and the differential displacement of the piston is equal to the differential change of volume. The integral J F dh is then equal to P dV. This relation is the only change that is made in Equation (2.15) or a similar equation for quasistatic processes. The frictional effects or the collisions result in a temperature increase either of the surroundings, or of both the system and surroundings as the case may be, or the effects may be interpreted in terms of heat, as discussed above. 

The differential of work related to volume changes is inexact for quasistatic processes. First, for quasistatic processes,... 

Equation (4.17) is applicable to quasistatic processes for the work of expansion and compression. On the introduction of the second law we have four equations for closed systems... 

As long as f1 and f2 in interacting systems differ, processes will go on which alter the prevailing values of xx and x2. The fact that ultimately xx and x2 become stationary does not mean that all forces now vanish, but rather that they precisely balance each other out. In quasistatic processes an infinitesimal difference between the applied (or driving) forces and the resistive forces is established, thus allowing the configuration of the system to change very slowly. 

The foregoing is a very elementary illustration of the fact that only in quasistatic processes is it permissible to replace the externally applied force by an oppositely directed internal force. If this can be done the internal force becomes a function of state of the system itself and thus, amenable to thermodynamic analysis. 

Quasistatic process. One that involves passage through a large succession of very closely spaced equilibrium states. In this process the surroundings may be altered such that on the return path to the original system configuration the universe ends up in a different state. 

Choose a particular quasistatic process that takes a given system from state 1... 

Krotov, V. V. and Rusanov, A. I., Quasistatic processes in liquid films. In Problems of the Thermodynamics of Heterogeneous Systems and of the Theory of Surface Phenomena. Vol. 2, pp. 147-178 Izd. Leningrad. Univ., Leningrad, 1973 [in Russian],... 

Figure 8. Quasistatic break-up. The chart on the left shows the width of the neck of simulated catenoid-hke interfaces as a function of the volume that is enclosed inside them. The plot on the right shows a quantitative comparison of the simulated - quasistatic - process with the experimental data for a range of parameters (Q,p, //, y) (Adapted from Ref. [21]).

In a real process the work done on a system exceeds that in a quasistatic process, provided the change in state is the same. In the real process part of the work is employed for spontaneous phenomena such as friction, reactions resulting from charge transfer etc. occurring inside the system. In the case of internal state changes the total work done on a system is given by... 

Also very important of course are processes leading from a metastable equilibrium state to a stable equilibrium state. These are irreversible, because when the (extra) constraint is released, even momentarily, the system is not in balance and proceeds in one direction, towards equilibrium. However, this inexorable progress towards equilibrium can be performed in one jump or can be halted in a succession of (metastable) equilibrium states called a quasistatic process. 

In many presentations of thermodynamics, quasistatic processes are either not mentioned or are said to be the same as reversible processes. In our usage, however, quasistatic processes are similar to reversible ones in that they are a continuous succession of equilibrium states, but these states are metastable equilibrium states, not stable equilibrium states. A quasistatic process is most easily imagined as resulting when one of the constraints on a metastable equilibrium state is released for an extremely short time, then re-imposed. While the constraint is released, the system changes slightly but irreversibly towards equilibrium, then settles down in its new metastable equilibrium state when the constraint is re-applied. This succession of events is repeated until the final state is reached. 

Thus, for example, the heat absorbed by the system in a quasistatic process involving a temperature change from Tq to T, at constant pressure, is given by... 

For reversible quasistatic processes and infinitesimal strains (3.76) then becomes... 

It is an imaginary, idealized process in which the system passes through a continuous sequence of equiUbrium states. That is, the state at each instant is one that in an isolated system would persist with no tendency to change over time. (This kind of proeess is sometimes called a quasistatic process.)... 

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