Question

According to Boltzmann’s statistical theory of entropy, if there are 100,000,000 possible states that a collection of gas particles can occupy in a closed box at a given instant, what is the entropy of that system?

Answer 1

Given that there the possible states are

$\text{W = 10}^8$

We have to find the entropy of the system.

According to Boltzmann's statistical theory of entropy,

$S=k_B\text{ ln W}$

Here, Boltzmann's constant is

$k_B\text{ = 1.38}\times10^{-23}\text{ J/K}$

Substituting the values, the entropy of the system will be

$\begin{gathered} S=\text{ 1.38}\times10^{-23}ln(10^8\text{)} \\ =\text{ }2.54\times10^{-22}\text{ J/K} \end{gathered}$