## Entropy And Disorder

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# Entropy and Disorder

To understand the term ‘disorder’, let us consider a system existing in a microstate having only one microstate i.e. W=1. This means that particles of the system can be arranged in only one way and in no other way. Thus in this state we have full and definite information about the particulars of the system. In such is said to be in perfect order. Theoretically, a system at 0

Let us now consider a microstate of the system for which W=2. Since, in this case, the system can exist in any of the two equally probable microstates, we cannot say with certainty on which of the two state systems exists at any instant of time. Thus there is a certain amount of loss of information about the system. In this case we can only say that the system can exist in either one of the two microstates with a probability=1/2. This statement of uncertainty or the loss of information about the state of a system is known as disorder.

It the system is in the microstate with W=3, then is a greater uncertainty (i.e., greater disorder) associated with the system because, it can now exist in any of the three microstates. The probability for it t be in a particular microstate is now reduced to 1/3. Thus increase in the value of W means increase in the amount of disorder or in other words, decreases in the amount of information as to which microstate the system occupies . Hence W can be taken as measure of the disorder in a system and is sometimes called the disorder number of a given microstate.

Further form the relation S = K In W, we see that the entropy is intimately connected with the disorder in the system and can be taken as a measure of disorder.

The law of increase of entropy (as studied in ‘thermodynamics’ in earlier classes) can thus also be stated as follows:

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^{0}K should be in a state perfect order.Let us now consider a microstate of the system for which W=2. Since, in this case, the system can exist in any of the two equally probable microstates, we cannot say with certainty on which of the two state systems exists at any instant of time. Thus there is a certain amount of loss of information about the system. In this case we can only say that the system can exist in either one of the two microstates with a probability=1/2. This statement of uncertainty or the loss of information about the state of a system is known as disorder.

It the system is in the microstate with W=3, then is a greater uncertainty (i.e., greater disorder) associated with the system because, it can now exist in any of the three microstates. The probability for it t be in a particular microstate is now reduced to 1/3. Thus increase in the value of W means increase in the amount of disorder or in other words, decreases in the amount of information as to which microstate the system occupies . Hence W can be taken as measure of the disorder in a system and is sometimes called the disorder number of a given microstate.

Further form the relation S = K In W, we see that the entropy is intimately connected with the disorder in the system and can be taken as a measure of disorder.

The law of increase of entropy (as studied in ‘thermodynamics’ in earlier classes) can thus also be stated as follows:

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