Relationship between W and Entropy

[abram_wassily_1G]

In looking at the course reader notes, I understand that the relationship between W and Entropy is explained by the Boltzmann equation, but how does this Boltzmann equation conceptually explain the relationship between W and Entropy? Thank you.

[Lauren_Johnston_3F]

Boltzmann's equation is a probability equation relating the entropy S of an ideal gas to the quantity W, the number of real microstates corresponding to the gas' macrostate. It shows the relationship between entropy and the number of ways the atoms or molecules of a thermodynamic system can be arranged and yet still give rise to the same total energy. Each arrangement of the molecules in the sample is in a different state (microstate) and W is equal to the number of different microstates that correspond to the same energy. When there are many energy levels accessible, the number of arrangements of molecules that result in the same energy and the corresponding entropy is large. It enables us to calculate the absolute entropy at any temperature.