Question

Calculate the change in entropy if the number of microstates of the system changes from 23 to 72. (Give your answer to three significant figures. Include the sign of the value in your answer.)

Boltzmann's equation is given below.

ΔS = k * ln (Wfinal/Winitial)

In this equation, ΔS is the change in entropy, Winitial is the initial number of microstates in the system, Wfinal is the final number of microstates in the system, and k is Boltzmann's constant, 1.3806503 ✕ 10−23 J/K.

Then state whether the entropy of the system increased or decreased.

Answer 1

Change in entropy = k * ln (Wfinal/Wintial)

Given Wintial = 23

Wfinal =72

K = 1.3806503*10-23 J/K

change in entropy = 1.3806503*10-23*ln(72/23) = 1.3806503*10-23*1.14117= 1.57559*10-23 J/K

Entropy is increased because change in entropy is positive if it is negative entropy decreases and other reason number of microstates increases from 23 to 72 that means system gets disturbed, entropy means dis orderness or distrubance in the system due to increase in microstates entropy increased.