Entropy, calculating changes

When calculating entropy changes, be careful about the sign of q, use the appropriate temperatures, and sum the changes for system and surroundings. 

A large portion of the calculated entropy change (+ or -) results from the relative ordering or disrupting of water structure during adsorption. 

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. 

Before we go on to calculate entropy changes for specific processes there are three matters which have been raised that we... 

Also from Frame 13 we have an equation for calculating entropy change in the form ... 

This is an example of a real process and it is not a reversible process since infinitesimal change in constraints cannot bring back the previous state of the system. How to calculate entropy change in such a process ... 

What determines whether a process under consideration will be spontaneous Where does a spontaneous process end How are energy, volume, and matter partitioned between the system and surroundings at equilibrium What is the nature of the final equilibrium state These questions cannot be answered by the first law. Their answers require the second law and properties of the entropy, and a few developments are necessary before we can address these questions. We define entropy by molecular motions in Section 13.2 and by macroscopic process variables in Section 13.3. Finally, we present the methods for calculating entropy changes and for predicting spontaneity in Section 13.5. 

Stated as an abstraction and generalization of engineering observations on the efficiency of heat engines. We start the discussion by presenting a nonmathematical qualitative summary of the arguments on efficiency. Then we define entropy and state the second law. Section 13.5 applies the definition to calculate entropy changes and to predict spontaneity of processes. 

This section outlines procedures for calculating entropy changes that occur in the system and in the surroundings during several types of processes. The final subsections show how entropy changes calculated for the thermodynamic universe (system plus surroundings) predict whether a particular contemplated process can occur spontaneously when attempted in the laboratory or in a chemical plant. 

To calculate entropy changes for chemical reactions, we find it convenient to use the same standard state already selected for enthalpy calculations in Section 12.3. For this purpose, we define the standard molar entropy to be the absolute molar entropy S° at 298.15 K and 1 atm pressure (Fig. 13.8) ... 

Tabulated standard molar entropies are used to calculate entropy changes in chemical reactions at 25°C and 1 atm, just as standard enthalpies of formation are combined to obtain enthalpies of reaction according to Hess s law (see Section 12.3). 

It is easy to calculate entropy changes for isothermal processes, because T is constant and comes outside the integral to give AS = q ev/T. A specific example is the isothermal compression or expansion of an ideal gas, for which AS = nR InlVf/V ). A second example is any phase transition at constant pressure for which q, y = The entropy change is then AS ang =... 

Table III - Experimental activation entropy AS and calculated entropy change ASp for the chain propagation in the free radical polymerization of some monomers.

Figure 1. Calculated entropy changes occurring in intramolecular cyclizations and intermolecular propagations.

In the laboratory we normally carry out unidirectional changes, that is, either ice to water or water to ice. We can calculate entropy change in each case using the equation AS = AH/T as long as the temperature remains at 0°C. The same procedure can be applied to the water-steam transition. In this case AH is the heat of vaporization and T is the boiling point of water. Example 18.5 examines the phase transitions in benzene. 

Calculate entropy changes in the surroundings for isothermal processes. (Section 19.4)... 

Calculate entropy changes of real fluids along special paths. 

With this result we have related entropy to measurable quantities (heat, temperature). We now have a simple methodology to calculate entropy changes between two states connect the states with a mechanically reversible path, and compute the quantity dQrev/r along a differential step. The change of entropy between the two states is the integral of this differential over the entire path ... 

The phase envelope in Fig. 1 below 8 atm, (36.33°K) was constructed using YendalPs saturated vapor curve and the calculated entropy change of vaporization. The upper portion of the phase envelope was constinicted by a trial-and-error method since these points as given by Yendall seemed to be in doubt. 

You can apply this kind of reasoning to help you judge whether a calculated entropy change has the correct sign. 

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