Entropy disorder and

The calculation of AS from equations (2.69) to (2,74), along with equations (2.78) or (2.79), all demonstrate that an increase in entropy causes an increase in disorder. For example  

On a molecular scale, expanding a gas causes the molecules to occupy a larger volume, leading to disorder. 

If T2 T, then AS 0 since Cp and T are 0. From a molecular point of view, heating a solid increases the amplitudes and energy distributions of the vibrations of the molecules in the solid, resulting in increased disorder. 

Since Afus// and T are 0, then AS 0. A liquid is less ordered than a solid. Hence, melting a solid leads to increased disorder. 

11 We will see later that this same equation applies to the mixing of liquids or solids when ideal solutions form. 

This simulated inconvertibility can be seen even more dramatically in any molecular system with an incommensurably large number of balls . 

One more example can be taken from a real problem of either the chemical or isotope separation of molecules. Let two different gases be divided by a partition. If the partition is removed, both gases will spontaneously become mixed. However, the return process of separation will not take place separation demands a huge expenditure of energy and effort. 

These examples show that any process aspires spontaneously to proceed to a state of greater disorder. This corresponds to the aspiration of a system to proceed to the state that has the greater entropy. The irreversibility of thermal processes corresponds to the irreversibility of order and disorder. Thus, entropy is a measure of the system s disorder. 

Despite its generality, the second law of thermodynamics has no absolute character. Deviations from it due to fluctuations are quite natural the fewer the number of particles, the greater the probability of deviations. Infringement of the second law is shown at small concentrations. 

The first and second laws of thermodynamic allow us to judge the behavior of thermodynamic systems near to absolute zero (0 K). This problem was formulated by Nemst 

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In equation (1.17), S is entropy, k is a constant known as the Boltzmann constant, and W is the thermodynamic probability. In Chapter 10 we will see how to calculate W. For now, it is sufficient to know that it is equal to the number of arrangements or microstates that a molecule can be in for a particular macrostate. Macrostates with many microstates are those of high probability. Hence, the name thermodynamic probability for W. But macrostates with many microstates are states of high disorder. Thus, on a molecular basis, W, and hence 5, is a measure of the disorder in the system. We will wait for the second law of thermodynamics to make quantitative calculations of AS, the change in S, at which time we will verify the relationship between entropy and disorder. For example, we will show that... 

In Chapter 1 we saw that the Boltzmann equation S = k log W gives the same qualitative relationship between entropy and disorder and suggested that a fundamental property of entropy is a measure of the disorder in a system. In Chapter 10 we will explore this relationship in more detail on the molecular level, and use the Boltzmann expression to develop quantitative relationships between entropy and disorder. 

One way to remember the relation between entropy and disorder is to consider a handful of chopsticks. Dropped on the floor, they are arranged randomly (a state of high entropy). Placed end-to-end in a straight line, they are arranged intentionally (a state of low entropy). The more disordered, random arrangement is favored and easier to achieve energetically. 

We can see the link between entropy and disorder by considering some specific examples. 

In addition, there is a relation between entropy and disorder disordered states have higher probabilities than ordered states. In general, the changes that are accompanied by an increase in entropy result in increased molecular disorder. Thus, entropy is also a measure of the molecular disorder of the state. Although disorder may be related to entropy qualitatively, the amount of disorder is a subjective concept and it is much better to relate entropy to probability rather than to disorder. Such concepts can be described in terms of thermodynamic probabilities (Q) in statistical mechanics. The entropy of a system is a function of the probability of the thermodynamic state of this system, S = /( 2). We know from statistical mathematics that only logarithmic functions satisfy probabilistic equations, so that we may use... 

Thus although there is a relationship betv een entropy and disorder, it is not always on the macroscopic scale, i.e., it does not always accord with what human observers would call disorder, especially when energy changes are involved. Nevertheless, it is... 

The easiest way to observe the connection between entropy and disorder is to study ideal gases. First, one defines the disorder as the thermodynamic probability W. the number of ways a system can be arranged (in contrast to the normally chosen probability that would be a fraction). Next, one notices that W is multiplicative. The combined probability of systems one and two is W = Wi x W2. The entropy, in contrast, is extensive, re. S = Si + S2. Any connection between the two must thus be ... 

It is clear that out of the systems completely different by their physical state, the entropy can be the same if their number of possible microstates corresponding to one maeroparameter (whatever parameter it is) coineide. Therefore the idea of entropy ean be used in various fields. The increasing self-organization of hiunan soeiety. .. leads to the increase in entropy and disorder in the environment that is demonstrated, in partieular, by a large number of disposal sites all over the earth [2]. 

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