Q1: A perfectly insulated container of volume V is divided into two equal halves by a partition. One side is under vacuum, while the other side has one mole of an ideal gas (with constant heat capacity) at 298 K. If the partition is broken, the final temperature of the gas in the container

ANS:C - will be less than 298 K.

When the partition is broken, the gas will expand into the vacuum side until it fills the entire volume of the container. This process is an irreversible adiabatic expansion because the container is perfectly insulated and there is no exchange of heat with the surroundings. During an adiabatic expansion, the gas performs work on its surroundings, leading to a decrease in its internal energy and temperature. Since the initial temperature of the gas is 298 K and it expands irreversibly, the final temperature of the gas will be less than 298 K. Therefore, the correct option is: "will be less than 298 K."