Final answer:
The entropy of an ideal gas increases during free expansion as it occupies a larger volume, creating more disorder and possible microstates without any heat exchange with the environment.
Step-by-step explanation:
The change in entropy of an ideal gas during free expansion can be described as follows. Consider an ideal gas confined to a volume V1. When the gas is allowed to undergo free expansion, it quickly fills a larger volume V2, without any heat exchange due to the walls of the container being thermally insulating.
This process is irreversible and increases the number of possible arrangements, or microstates, for the gas molecules, thereby increasing the system's disorder. The change in entropy (ΔS) can be calculated using the equation ΔS = nR ln(V2/V1), where n is the number of moles of gas and R is the universal gas constant. Because V2 is greater than V1, the entropy of the gas increases (ΔS > 0), which is also confirmed by the spontaneous nature of the expansion.