A system in a certain macrostate has 1.2 × 10³ microstates. Through some process, the system changes the number of microstates to 3 × 10⁴. What is the change in entropy for the process? A) 1.1 × 10⁻²³ J/K B) 2.1 × 10⁻²³ J/K C) 4.4 × 10⁻²³ J/K D) 5.6 × 10⁻²³ J/K

Question

Quizplus · Accepted Answer

The change in entropy ΔS is given by:
ΔS = k ln(Nf/Ni)
where k is the Boltzmann constant, Ni is the initial number of microstates, and Nf is the final number of microstates.

Plugging in the values given in the problem, we get:
ΔS = k ln(3 × 10^14/1.2 × 10^13) 
ΔS = k ln(25) 
ΔS = k × 3.21887 
ΔS = 4.4 × 10^-23 J/K

Therefore, the correct answer is C.

A System in a Certain Macrostate Has 1