Question

In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of ΔS (entropy)?

a. ΔS is positive
b. ΔS is negative
c. ΔS is zero

Answer 1

For a spontaneous process that decreases the number of microstates, the change in entropy (ΔS) is negative, indicating an increase in order within the system.

Step-by-step explanation:

If a spontaneous process results in a decrease in the number of microstates available to the system, we can conclude that the change in entropy (ΔS) for the system is negative. In thermodynamics, entropy is a measure of the number of microstates that are available to a system at a given energy. If the number of microstates decreases, it signifies that the system has become more ordered, and hence the total number of ways the system can be arranged has reduced, leading to a decrease in entropy (ΔS < 0). This is consistent with the molecular-scale interpretation of entropy, which relates entropy to the probability of the occurrence of a process. In contrast, an increase in microstates would result in positive ΔS.