Dropped on the floor, they are arranged randomly (a state of high entropy). One way to remember the relation between entropy and disorder is to consider a handful of chopsticks. 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. 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. 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. Thus, on a molecular basis, W, and hence 5, is a measure of the disorder in the system. But macrostates with many microstates are states of high disorder. Hence, the name thermodynamic probability for W. Macrostates with many microstates are those of high probability. 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. In Chapter 10 we will see how to calculate W. In equation (1.17), S is entropy, k is a constant known as the Boltzmann constant, and W is the thermodynamic probability. The first and second laws of thermodynamic allow us to judge the behavior of thermodynamic systems near to absolute zero (0 K). Infringement of the second law is shown at small concentrations. Deviations from it due to fluctuations are quite natural the fewer the number of particles, the greater the probability of deviations. ĭespite its generality, the second law of thermodynamics has no absolute character. Thus, entropy is a measure of the system s disorder. The irreversibility of thermal processes corresponds to the irreversibility of order and disorder. This corresponds to the aspiration of a system to proceed to the state that has the greater entropy. These examples show that any process aspires spontaneously to proceed to a state of greater disorder. However, the return process of separation will not take place separation demands a huge expenditure of energy and effort. If the partition is removed, both gases will spontaneously become mixed. Let two different gases be divided by a partition. One more example can be taken from a real problem of either the chemical or isotope separation of molecules. This simulated inconvertibility can be seen even more dramatically in any molecular system with an incommensurably large number of balls. ġ1 We will see later that this same equation applies to the mixing of liquids or solids when ideal solutions form. Hence, melting a solid leads to increased disorder. 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. On a molecular scale, expanding a gas causes the molecules to occupy a larger volume, leading to disorder. 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.
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