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A microscopic perspective, in statistical thermodynamics the entropy is a measure of the number of microscopic configurations that are capable of yielding the observed macroscopic description of the thermodynamic system:

S=KBln Ω

where Ω is the number of microscopic configurations, and KB is Boltzmann's constant. It can be shown that this definition of entropy, sometimes referred to as Boltzmann's postulate, reproduces all of the properties of the entropy of classical thermodynamics(shahbaz)

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A microscopic perspective, in statistical thermodynamics the entropy is a measure of the number of microscopic configurations that are capable of yielding the observed macroscopic description of the thermodynamic system:

S=KBln Ω

where Ω is the number of microscopic configurations, and KB is Boltzmann's constant. It can be shown that this definition of entropy, sometimes referred to as Boltzmann's postulate, reproduces all of the properties of the entropy of classical thermodynamics(shahbaz)

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It's not so much a matter of justifying it as recognizing that the function δq/T has been assigned the name "entropy" - specifically:

dS = δq/T (by definition)

The quantity δq/T was assigned a name because it is so useful in thermodyanmics for predicting direction of heat flow, efficiency of cycles, and natural (spontaneous) processes.

The idea that entropy is a measure of disorder comes from the proof by by Ludwig Boltzmann in the 1870s who analyzed the statistical behavior of the microscopic components of system. Boltzmann showed that the statistical-mechanical definition of entropy was equivalent to the thermodynamic entropy to within a constant number which has since been known as Boltzmann's constant.

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  • The Boltzmann constant (kB or k), named after Ludwig Boltzmann, is a physical constant relating energy at the individual particle level with temperature.
  • It is the gas constant R divided by the Avogadro constant
  • It has the same dimension (energy divided by temperature) as entropy. The accepted value in SI units is 1.3806488(13)×10−23 Joule/degree K
  • For more information refer to link below.
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Ludwig Boltzmann was born on February 20, 1844.

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Ludwig Boltzmann was born on February 20, 1844.

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