Entropy change definition

It must be emphasised that the heat q which appears in the definition of entropy (equation 20.137) is always that absorbed (or evolved) when the process is conducted reversibly. If the process is conducted irreversibly and the heat absorbed is q, then q will be less than q, and q/T will be less than AS the entropy change (equation 20.137). It follows that if an irreversible process takes place between the temperatures Tj and 7 , and has the same heat intake q at the higher temperature 7 2 as the corresponding reversible process, the efficiency of the former must be less than that of the latter, i.e. 

The expressions in Eq. 1 and Eq. 6 are two different definitions of entropy. The first was established by considerations of the behavior of bulk matter and the second by statistical analysis of molecular behavior. To verify that the two definitions are essentially the same we need to show that the entropy changes predicted by Eq. 6 are the same as those deduced from Eq. 1. To do so, we will show that the Boltzmann formula predicts the correct form of the volume dependence of the entropy of an ideal gas (Eq. 3a). More detailed calculations show that the two definitions are consistent with each other in every respect. In the process of developing these ideas, we shall also deepen our understanding of what we mean by disorder. ... 

Thus, the steric factor may be explained with the help of entropy change. When two molecules come together to produce the activated complex, the total translational degrees of freedom are reduced (from 6 to 3) and rotational degrees of freedom also diminish. This is compensated by an increase in vibrational degrees of freedom. But the definite orientation in forming the activated complex necessarily reduced the entropy, i.e. AS is negative. This decrease in entropy is small when reaction takes place between simple atoms. The calculated value of kbT/h corresponds to collision frequency... 

The definition of entropy requires that information about a reversible path be available to calculate an entropy change. To obtain the change of entropy in an irreversible process, it is necessary to discover a reversible path between the same initial and final states. As S is a state function, AS is the same for the irreversible as for the reversible process. 

Often, it is difficult to distinguish definitely between inner sphere and outer sphere complexes in the same system. Based on the preceding discussion of the thermodynamic parameters, AH and AS values can be used, with cation, to obtain insight into the outer vs. inner sphere nature of metal complexes. For inner sphere complexation, the hydration sphere is disrupted more extensively and the net entropy and enthalpy changes are usually positive. In outer sphere complexes, the dehydration sphere is less disrupted. The net enthalpy and entropy changes are negative due to the complexation with its decrease in randomness without a compensatory disruption of the hydration spheres. 

Following this, the thermodynamic arguments needed for determining CMC are discussed (Section 8.5). Here, we describe two approaches, namely, the mass action model (based on treating micellization as a chemical reaction ) and the phase equilibrium model (which treats micellization as a phase separation phenomenon). The entropy change due to micellization and the concept of hydrophobic effect are also described, along with the definition of thermodynamic standard states. 

When a chemical reaction is proceeding, it is, by definition, not at equilibrium and thus not reversible. Thus, entropy changes in chemical reactions cannot be obtained from heat effects in calorimetric experiments. Entropy changes can be obtained by studying chemical equilibrium (Chapter 7) or by opposing the tendency of the reaction to proceed with an applied electric potential (Chapter 10). 

At this temperature, the entropy change for dissolution of liquid hydrocarbons in water is zero. However, the entropy of protein denaturation is far from zero at this temperature but amounts to 17.6 J - K l per mole of amino acid residues (Privalov, 1979), a value that corresponds to an 8-fold increase of the number of possible configurations and is close to the value expected for the helix-coil transition of polypeptides (Schellman, 1955). This difference shows that an oil drop is an inadequate model for a globular protein. A more suitable model resembles that of a small crystal with a quite definite positive melting entropy (see also Bellow, 1977, 1978). 

Entropy change for a given state is a definite quantity, independent of the fact whether the change is brought about reversibly or irreversibly. However, mathematically it is given by equation,... 

By definition, W = 0 A V = 0 AE = Qt. Note that the curvatures of the constant-volume line on the T-S chart (Fig. 19.3) are different from the constant-pressure line (Fig. 19.2). Adding heat (i to a constant-volume process affects only the internal energy. The total entropy change must take into account the total steam mass m = 5 lb (2.3 kg). 

This very important relationship is the macroscopic (thermodynamic) definition of AS. In our treatment we started with the definition of entropy based on probability, because that definition better emphasizes the fundamental character of entropy. However, it is also very important to know how entropy changes relate to changes in macroscopic properties, such as volume and heat, because these changes are relatively easy to measure. 

We also generalize the definition of heat Q as the deficit function needed so that dQ — (dE — dW — "J i l i dn ) vanishes identically, in order that E remains a function of state. We then view the entropy change as being given by... 

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. 

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