Entropy change in irreversible

The Caratheodory analysis has shown that a fundamental aspect of the Second Law is that the allowed entropy changes in irreversible adiabatic processes can occur in only one direction. Whether the allowed direction is increasing or decreasing turns out to be inherent in the conventions we adopt for heat and temperature as we will now show. 

Fiolitakis, E., Some Aspects on the Entropy Change in Onsa-ger s Sense for Irreversible Chemical Processes, to be published... 

To determine the entropy change in this irreversible adiabatic process, it is necessary to find a reversible path from a to b. An infinite number of reversible paths are possible, and two are illustrated by the dashed lines in Figure 6.7. 

Calculation of the entropy produced in systems undergoing different flow processes (called irreversible processes) is key for considering steady-state systems. In order to measure the entropy produced in the system, we think of it as transported to the surroundings in a reversible manner and measure the entropy changes in the surroundings. From Eqs. (5) and (7),... 

Here, <55 s 0 is the entropy change arising from irreversible processes occurring within a completely closed system. As Eq. (1.12.9a) shows, S can then only increase. As soon as these processes have ceased, 50 = 55 = 0, so that 5 has assumed an extremal value which is a maximum under the present constraints. For example, the entropy change in the free expansion of a gas can be determined by finding AS under quasistatic conditions, as specified later in Section 2.3. Since 5 is a function of state the same entropy change takes place in a free expansion under the same conditions. All this, of course, merely repeats what has been well established in earlier sections. 

We shall now show that mixing is not an irreversible process, and the entropy change, in the process depicted in figure H.l, is not due to the mixing process, but to expansion. Therefore, the reference to the quantity (H.10) or (H.12) as entropy of mixing is inappropriate and should be avoided. 

Thus as the entropy change in the gas is the same in both cases we must investigate the surroundings before we can decide whether a change has occurred in a reversible or an irreversible manner. This restricts the usefulness of entropy in defining equilibrium conditions. 

In order to calculate the entropy changes in the two reservoirs after this irreversible process has occurred, we must devise a way of transferring the heat reversibly, since an entropy change can be calculated directly only for a reversible process. We can make use of an ideal gas to carry out the heat transfer process, as shown in Figure 5.56. The gas is contained in a cylinder with a piston. We first place it in the warm reservoir, at temperature Ti, and expand it reversibly and isothermally until it has taken up heat equal to q. The gas is then removed from the hot reservoir, placed in an insulated container, and allowed to expand reversibly and adiabatically until its temperature has fallen to T. Finally, the gas is placed in contact with the colder reservoir at Tc and compressed isothermally until it has given up heat equal to q. 

Here is the CL thermal conductivity (W m K ) and the source terms Rs, Rr, and Rj describe the rate of heating due to entropy change in the electrochemical reaction, irreversible heating due to proton transport through the double layer at the metal/electrolyte interface and Joule heating, respectively. 

Figure 3.7 Entropy changes in a system consist of two parts d S due to irreversible processes, and dgS, due to exchange of energy and matter. According to the second law, the change diS is always positive. The entropy change d S can be positive or negative...

For the same step executed irreversibly (i), with the temperature of the system at T and that of the surroundings at Tq, the resulting heat exchange AiQ = —ArQo produces an entropy change in the... 

Concerning the use of Eq. (1.10.2c), in conformity with earlier statements, since Eq. (1.10.2c) relates only to reversible processes, while dS refers to the total entropy change. For irreversible processes Eq. (1.10.2a) or (1.10.2b) must be used. Similar caveats hold for the remaining differential equations for functions of state introduced below. 

The entropy of a system changes both in reversible and in irreversible processes, but reasonably entropy changes in the latter should be larger than in the former. 

Thus, the total entropy change in a given process - multiplied by the temperature of the surroundings- represents the measure of the work lost in this process as a result of the irreversibilities involved entropy becomes the yardstick of lost mechanical energy. 

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