## Statistical Entropy

**Statistical Entropy**:The application of probability theory to the principle of entropy in thermodynamicis. This shows entropy ito be a measure of the amount of disorder in a system. The mathematical relationship is as follows.

- The number of equivalent microstates (number of possible ways a given condition to occur) is denoted as W.
- Entropy is denoted as S
- k is the Boltzmann Constant = 1.38 X 10
^{-23}JL^{-1}

# S = k ln W

The larger W is the more disordered the system and the larger a system’s entropy.

The smaller W is the more ordered the system is the more disordered it is and the smaller a system’s entropy.## The Second Law of Thermodynamics

The Second Law of Thermodynamics indicates that entropy tends to increase and because entropy is related to disorder, it also indicates that a system’s degree of disorder tends to increase. The only way to decrease a system’s entropy and increase its order is for work to be performed on the system. Now the Second Law of thermodynamics shows that energy applied a system can reduce its entropy but it does not show how the manner in which energy is applied affects entropy that is it does not show the deference between construction work and a bomb. Getting order from disorder requires an additional principle, a principle that relates entropy and energy.

## Order from Disorder

This additional principle is based on the relationship between the degree of order or disorder with which energy is applied to a system and the degree of order or disorder that it produces in that system.

The result is that energy applied to a system in a manner more ordered than that system’s degree of order increases the system’s order and decreases its entropy. On the other hand energy applied to a system in a manner more disordered than that system’s degree of disorder increases the system’s disorder and increases its entropy. The mathematical relationship is as follows.

- .Number of equivalent microstates of the applied energy is W
_{e }. - Number of initial equivalent microstates of the system is W
_{s }. - The change in entropy is denoted as DS.
- k is the Boltzmann Constant = 1.38 X 10
^{-23}JL^{-1}.

This shows the general direction that applying energy to a system will move the entropy of that system as well as the maximum change in the systems entropy but the actual change in entropy results from the amount of energy actually applied to the system .

Reduced to it simplest form this principle can be described in two statements:

- The general application of energy to a system in a manner more random than that system will increase the entropy of that system.
- The general application of energy to a system in a manner less random than that system will decrease the entropy of that system.

This shows the difference between construction work and a bomb because construction work is less random than that of the raw material and so it decreases its entropy. By contrast a bomb explosion is more random than that of the raw material so it decreases its entropy.

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