Entropy Changes in a System

As we said earlier, entropy often is described as a measure of randomness or disorder. Although this can be a useful description, it should be used with caution and not taken too literally. It is generally preferable to view the change in entropy of a system in terms of the change in the number of microstates of the system. Nevertheless, we can use the concept of disorder to make some qualitative predictions about the entropy changes that accompany certain processes. 

Therefore, this order------- disorder phase transition results in an increase in entropy because 

Sample Problem 18.1 lets you practice the qualitative prediction of entropy change for a process. 

For each process, determine the sign of A5 for the system (a) decomposition of CaCOj(s) to give CaO(s) and COifg), (b) heating bromine vapor from 45°C to 80°C, (c) condensation of water vapor on a cold surface, (d) reaction of NH tg) and HCl(g) to give NHjCKj), and (e) dissolution of sugar in water. 

Strategy Consider the change in numher of mierostates (the number of possible positions that each particle can occupy) in each case. An increase in the numbo of mierostates corresponds to an increase in entropy and therefore a positive AS. 

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While the first law allows us to calculate the energy change associated with a given process, it says nothing about whether or not the process itself will take place spontaneously. This is the province of the second law of thermodynamics and leads to the introduction of another state function, entropy, S. The entropy change in a system which moves from state 1 to state 2 is defined by... 

We can use tabulated absolute entropy values to calculate the standard entropy change in a system, such as a chemical reaction, as just described. But what about the entropy change in the surroundings We encountered this situation in Section 19.2, but it is good to revisit it now that we are examining chemical reactions. 

The entropy change in a system undergoing a process (1 — 2) is thermodynamically formulated in terms of the heat q taken up by that system and the temperature T at which the heat uptake occurs ... 

The Second Law can therefore be stated as The total entropy change in a system resulting from any real processes in the system is positive and approaches a limiting value of zero for any process that approaches reversibility (Themelis, 1995). The entropy of a reversible process is equal to the heat absorbed during the process, divided by the temperature at which the heat is absorbed (Equation 9.3). Reversibility denotes a process which is carried out under near-equilibrium conditions and therefore means that it is carried out most efficiently. Combining the First Law and the Second Law gives the expression... 

If Cp is known rather than Cv, integrate dS = (Cp/T)dT instead to get AS = CplniTg/TA). Notice that the entropy change in a system will be different depending on whether the pressure or the volume is held constant because in... 

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...

To illustrate how Gibbs approach allows us to solve thermodynamic problems, let us consider entropy change in a system under isothermal (constant temperature) conditions. If we follow the older technique, we have to devise a process by which a system expands at constant temperature, which would imdoubtedly involve some assumptions regarding the nature of the substance and the apparatus. In Gibbs method this result falls simply out of a differential equation characterizing the appropriate surface. Technical aspects are given in Box 4... 

The following pictures show a molecular visualization of a system undergoing a spontaneous change. Account for the spontaneity of the process in terms of the entropy changes in the system and the surroundings. 

In thermodynamics, entropy enjoys the status as an infallible criterion of spontaneity. The concept of entropy could be used to determine whether or not a given process would take place spontaneously. It has been found that in a natural or spontaneous process there would be an increase in the entropy of the system. This is the most general criterion of spontaneity that thermodynamics offers however, to use this concept one must consider the entropy change in a process under the condition of constant volume and internal energy. Though infallible, entropy is thus not a very convenient criterion. There have, therefore, been attempts to find more suitable thermodynamic functions that would be of greater practical... 

Lu, N. Kofke, D. A. Woolf, T. B., Staging is more important than perturbation method for computation of enthalpy and entropy changes in complex systems, J. Phys. Chem. B 2003,107, 5598-5611... 

The fundamental question in transport theory is Can one describe processes in nonequilibrium systems with the help of (local) thermodynamic functions of state (thermodynamic variables) This question can only be checked experimentally. On an atomic level, statistical mechanics is the appropriate theory. Since the entropy, 5, is the characteristic function for the formulation of equilibria (in a closed system), the deviation, SS, from the equilibrium value, S0, is the function which we need to use for the description of non-equilibria. Since we are interested in processes (i.e., changes in a system over time), the entropy production rate a = SS is the relevant function in irreversible thermodynamics. Irreversible processes involve linear reactions (rates 55) as well as nonlinear ones. We will be mainly concerned with processes that occur near equilibrium and so we can linearize the kinetic equations. The early development of this theory was mainly due to the Norwegian Lars Onsager. Let us regard the entropy S(a,/3,. ..) as a function of the (extensive) state variables a,/ ,. .. .which are either constant (fi,.. .) or can be controlled and measured (a). In terms of the entropy production rate, we have (9a/0f=a)... 

Two factors determine the spontaneity of a chemical or physical change in a system a release or absorption of heat (AH) and an increase or decrease in molecular randomness (AS). To decide whether a process is spontaneous, both enthalpy and entropy changes must be taken into account ... 

In order to usefully apply the second law, it will be necessary to be able to calculate both AS, the entropy change in the system of interest, and A,S sur, the entropy change of the surroundings. (Thermodynamic functions without the subscript sur can be assumed to refer to the system.) The mathematical form of our second law then becomes... 

Because it takes some practice to be able to use the recipes for calculating entropy changes in the system and surroundings, a few simple examples are presented here. 

However, it is very difficult to measure the entropy change of a system and its surroundings in a biological process (i.e., processes occurring in plants and animals). Later in this chapter, a new thermodynamic term, free energy, will be used to describe the spontaneity of a process. 

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