Changes of state, irreversible

The entropy of a thermally isolated system can only increase in a natural (irreversible) change of state... 

The box includes three distinct parts. First, there is the assertion that a property called entropy, S, is an extensive state function. Second, there is an equation for calculating the entropy change of a closed system during a reversible change of state d5 is equal to dq/Tb. Third, there is a criterion for spontaneity d5 is greater than dq/Tb during an irreversible change of state. The temperature Tb is a thermodynamic temperature, which will be defined in Sec. 4.3.4. 

Irreversible Changes of State. — The dehydration of the hydrogel of silicic acid along the curve presents two important questions. 

Figure 2.27. An irreversible change of state in a gas cannot be depicted in a pV diagram. During the process the gas is in a state of nonequilibrium the gas is located, so to speak, at several points in the pV diagram at the same time. Therefore, the process cannot be described by the usual macroscopic state variables (see also fig. 2.4).

Once more it shall be noted that although AS has been determined for a reversible, isothermal change of state, (4.22), it also applies to an arbitrary reversible or irreversible change of state between the specified states of equilibrium (1) and (2) this is a consequence of the fact that the entropy 5 is a state function. Generally, the entropy S of gases increases with increasing dilution, i.e. when the volume Y is increased or when the pressure p is reduced. This is because the entropy 5 is a measure of the degree of disorder at molecular level. As will be seen in section 4.10, the molecular disorder, and thus the entropy, increases when crystalline substances melt and when liquids evaporate - i.e. by phase transformations that lead to increased disorder at molecular level. 

Sols without electrolytic character, which exhibit irreversible changes of state 56... 

We may contrast this result for A totai with that for Al/totai for an ideal gas, as mentioned in Section 5.1. In the irreversible expansion of an ideal gas, Allgys = 0 the surroundings undergo no change of state (Q and W are both equal to zero), and hence, A /total = 0- ff we consider the reversible expansion of the ideal gas, AUsys is also equal to zero and AUsun is equal to zero because Q = —W, so again A /total = 0- Clearly, in contrast to AS, AU does not discriminate between a reversible and an irreversible transformation. 

A reversible adiabatic expansion of an ideal gas has a zero entropy change, and an irreversible adiabatic expansion of the same gas from the same initial state to the same final volume has a positive entropy change. This statement may seem to be inconsistent with the statement that 5 is a thermodynamic property. The resolution of the discrepancy is that the two changes do not constitute the same change of state the final temperature of the reversible adiabatic expansion is lower than the final temperature of the irreversible adiabatic expansion (as in path 2 in Fig. 6.7). 

An interesting alternative demonstration of Equation (7.75) can be carried out on the basis of isothermal cycles and of the Kelvin-Planck statement of the second law. Consider two possible methods of going from State a to State b, a spontaneous change of state, in an isothermal fashion (Fig. 7.1) (1) a reversible process and (2) an irreversible process. 

The distinction between reversible and irreversible work is one of the most important in thermodynamics. We shall first illustrate this distinction by means of a specific numerical example, in which a specified system undergoes a certain change of state by three distinct paths approaching the idealized reversible limit. Later, we introduce a formal definition for reversible work that summarizes and generalizes what has been learned from the path dependence in the three cases. In each case, we shall evaluate the integrated work w 2 from the basic path integral,... 

For this purpose, consider a change of state A —> B, which can be achieved by either a reversible path (with heat qmy and work wrev) or an irreversible path (with heat girrev and work wirrevX as shown schematically below ... 

Note that to solve any problem involving an irreversible process, you should first evaluate the equivalent change of state for a reversible process, where the differentials can be easily integrated from initial to final state.)... 

A third statement of the second law is based on the entropy. In reversible systems all forces must be opposed by equal and opposite forces. Consequently, in an isolated system any change of state by reversible processes must take place under equilibrium conditions. Changes of state that occur in an isolated system by irreversible processes must of necessity be spontaneous or natural processes. For all such processes in an isolated system, the entropy increases. Clausius expressed the second law as The entropy of the universe is always increasing to a maximum. Planck has given a more general statement of the second law Every physical and chemical process in nature takes place in such a way as to increase the sum of the entropies of all bodies taking any part in the process. In the limit, i.e., for reversible processes, the sum of the entropies remains unchanged. 

It is a general observation that any system that is not in equilibrium will approach equilibrium when left to itself. Such changes of state that take place in an isolated system do so by irreversible processes. However, when a change of state occurs in an isolated system by an irreversible process, the entropy change is always positive (i.e., the entropy increases). Consequently, as the system approaches equilibrium, the entropy increases and will continue to do so until it obtains the largest value consistent with the energy of the system. Thus, if the system is already at equilibrium, the entropy of the system can only decrease or remain unchanged for any possible variation as discussed in Section 5.1. 

The work of an irreversible process is calculated by a two-step procedure. First, W is determined for a mechanically reversible process that accomplishes the same change of state. Second, this result is multiplied or divided by an efficiency to give the actual work. If the process produces work, the reversible value is too large and must be multiplied by an efficiency. If the process requires work, the reversible value is too smalt and must be divided by an efficiency. 

Repeat these calculations for exactly the same changes of state accomplished irreversibly with an efficiency for each process of 80 percent compared with the corresponding mechanically reversible process. 

When a system undergoes an irreversible process from one equilibrium state to another, the entropy change of the system AS is stilt evaluated by Eq. (A). In this case Eq. (A) is applied to an arbitrarily chosen reversible process that accomplishes the same change of state. Integration is not carried out for the original irreversible path. Since entropy is a state function, the entropy changes of the irreversible and reversible processes are identical. 

If these processes are carried out irreversibly but so as to accomplish exactly the same changes of state (i.e., the same changes in P, T, U, and H), then the values of Q and IT are different. Calculate values of Q and W for an efficiency of 80 percent for eacji step. 

If the same changes of state are carried out by irreversible processes, the property changes for the steps are identical with those already calculated. However, the values of Q and W are different. 

This equation is based on the assumption that the change of state resulting from the process is accomplished reversibly. However, the viscous nature of real fluids induces fluid friction that makes changes of state in flow processes inherently irreversible because of the dissipation of mechanical energy into internal energy. In order to correct for this, we add to the equation a friction term F. The mechanical-energy balance is then written ... 

Example 1.3 Entropy and distribution of probability Entropy is a state function. Its foundation is macroscopic and directly related to macroscopic changes. Such changes are mostly irreversible and time asymmetric. Contrary to this, the laws of classical and quantum mechanics are time symmetric, so that a change between states 1 and 2 is reversible. On the other hand, macroscopic and microscopic changes are related in a way that, for example, an irreversible change of heat flow is a direct consequence of the collision of particles that is described by the laws of mechanics. Boltzmann showed that the entropy of a macroscopic state is proportional to the number of configurations fl of microscopic states a system can have... 

---