A system in a certain macrostate has $1.2 \times 10^{3}$ microstates. Through some process, the system changes the number of microstates to $3 \times 10^{4}$. What is the change in entropy for the process?

Question

Quizplus · Accepted Answer

The change in entropy is given by $\Delta S = k \ln \frac{W_f}{W_i}$, where $k$ is Boltzmann's constant, $W_f$ is the final number of microstates, and $W_i$ is the initial number of microstates. Plugging in the given values, we get $\Delta S = (1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}) \ln \frac{3 \times 10^{4}}{1.2 \times 10^{3}} = 4.4 \times 10^{-23} \mathrm{~J} / \mathrm{K}$.

A System in a Certain Macrostate Has 1.2×1031.2 \times 10^{3}1.2×103 Microstates 3×1043 \times 10^{4}3×104

A System in a Certain Macrostate Has $1.2 \times 10^{3}$ Microstates $3 \times 10^{4}$