Changes, irreversible

It is still necessary to consider the role of entropy m irreversible changes. To do this we return to the system considered earlier in section A2.1.4.2. the one composed of two subsystems in themial contact, each coupled with the outside tliroiigh movable adiabatic walls. Earlier this system was described as a function of tliree independent variables, F , and 0 (or 7). Now, instead of the temperature, the entropy S = +. S P will be... 

This is frequently stated for an isolated system, but the same statement about an adiabatic system is broader.) A2.1.4.6 IRREVERSIBLE CHANGES AND THE MEASUREMENT OF ENTROPY... 

Figure A2.1.5. Irreversible changes. Two gases at different pressures separated by a diathemiic wall, a piston that can be released by removing a stop (pin).

The assumption (frequently unstated) underlying equations (A2.1.19) and equation (A2.1.20) for the measurement of irreversible work and heat is this in the surroundings, which will be called subsystem p, internal equilibrium (unifomi T, p and //f diroughout the subsystem i.e. no temperature, pressure or concentration gradients) is maintained tliroughout the period of time in which the irreversible changes are... 

Now, as has been shown, q = TASior an isothennal reversible process only for an isothennal irreversible process AS = A S + Aj.S, and q = TA S. Since Aj.S is positive for irreversible changes and zero only for reversible processes, one concludes... 

Thermal stability. The tliennal stability of SAMs is, similarly to LB films, an important parameter for potential applications. It was found tliat SA films containing alkyl chains show some stability before an increase in tire number of gauche confonnations occurs, resulting in melting and irreversible changes in tire film. The disordering of tire... 

Because catalyst surfaces are reactive and often sensitive to their environments, they may be irreversibly changed by exposure to undesired reactants. Upsets in plant operations can lead to catastrophic losses of whole catalyst charges. A large catalyst charge that is mined can cost hundreds of thousands of dollars as well as the cost of lost operation. 

Numerous resistance measurements have been carried out under high-pressure shock compression [79D01]. Most of the work has been motivated by the desire to develop stress gauges to measure pressures in shock-compressed materials. Other measurements were undertaken to determine critical pressures to induce phase transformations. Although most of the work is not carried out in sufficient detail to relate resistance observations to defect characterizations, excess resistance at given shock pressures is observed in every case compared to comparably loaded static pressure observations. The presence of residual resistance for times after the loading is removed provides explicit evidence for irreversible changes in resistance due to defects. 

The radiation chemistry has been mainly discussed in terms of degradation reactions (as above) involving the loss of gaseous products and the irreversible change of the stoichiometry [203]. However, more recent results showed that polymers irradiated with radiation deposit-... 

A further increase in extension leads to irreversible changes which immediately precede the transition of the polymer into the oriented state. During this transition, the spherulites undergo considerable structural changes and are thus converted qualitatively into different structural elements i.e. macrofibrils4). After a certain critical elongation has been attained, the initial crystallites collapse and melt and a new oriented structure is formed in which the c axes of crystals are oriented in the direction of extension. 

All discussions of transport processes currently available in the literature are based on perturbation theory methods applied to kinetic pictures of micro-scattering processes within the macrosystem of interest. These methods do involve time-dependent hamiltonians in the sense that the interaction operates only during collisions, while the wave functions are known only before and after the collision. However these interactions are purely internal, and their time-dependence is essentially implicit the over-all hamiltonian of the entire system, such as the interaction term in Eq. (8-159) is not time-dependent, and such micro-scattering processes cannot lead to irreversible changes of thermodynamic (ensemble average) properties. 

It must be emphasised that this holds good only for reversible changes. To give three instances of increase of entropy in adiabatic irreversible changes we may cite ... 

Now if any irreversible changes occur in the system itself during the execution of the cycle, the principle of dissipation of energy shows that the available energy will be diminished in virtue of these, and since the available energy of the system must be the same after as it was before the execution of the cycle, because the state of the system is unaltered, it follows that some available energy must have been absorbed from outside in connection with the absorption of heat hence (A ) and therefore also... 

Relations (5) and (6) are combined in (4). Inequality (6) shows that if a system undergoes any irreversible change, there will have been a positive amount of entropy generated in the system itself during that change, since the entropy absorbed from outside is always less than the amount by which the entropy of... 

If the system is not isolated, its entropy may either increase or decrease. Thus, if a mass of gas is compressed in a cylinder impervious to heat, its entropy increases, but if heat is allowed to pass out into a medium, the entropy of the gas may decrease. By including the"gas and medium in a larger isolated system, we can apply (10) of 45, and hence show Jhat the medium gains more entropy than the gas loses. An extended assimilation of this kind shows that, if every body affected in a change is taken into account, the entropy of the whole must increase by reason of irreversible changes occurring in it. This is evidently what Clausius (1854) had in mind in the formulation of his famous aphorism The entropy of the universe strives towards a maximum. The word universe is to be understood in the sense of an ultimately isolated system. 

Persistently high operating temperatures lead to irreversible changes in the structure of the steel and eventual failure. 

Since this relation is in terms of properties of the system, it must also apply to a system in motion and to irreversible changes where the only work done is the result of change of volume. 

In any irreversible change, the overall disorder of the system and its surroundings increases, which means that the number of microstates increases. If W increases, then so does In W, and the statistical entropy increases, too. 

FIGURE 7.21 The changes in entropy and internal energy when an ideal gas undergoes (a) reversible and (b) irreversible changes between the same two states, as described in Example 7.12. 

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