Two moles of an ideal gas occupy a volume $V$. The gas expands isothermally and reversibly to a volume $3V$. Is the velocity distribution changed by the isothermal expansion? Explain.

You decide to take a nice hot bath but discover that your thoughtless roommate has used up most of the hot water. You fill the tub with $195$ kg of $30.0$°C water and attempt to warm it further by pouring in $5.00$ kg of boiling water from the stove. Is this a reversible or an irreversible process? Use physical reasoning to explain.

A lonely party balloon with a volume of $2.40$ L and containing $0.100$ mol of air is left behind to drift in the temporarily uninhabited and depressurized International Space Station. Sunlight coming through a porthole heats and explodes the balloon, causing the air in it to undergo a free expansion into the empty station, whose total volume is $425$ m³. Calculate the entropy change of the air during the expansion.

You make tea with $0.250$ kg of $85.0$°C water and let it cool to room temperature ($20.0$°C). Calculate the entropy change of the water while it cools.

A $15.0$-kg block of ice at $0.0$°C melts to liquid water at $0.0$°C inside a large room at $20.0$°C. Treat the ice and the room as an isolated system, and assume that the room is large enough for its temperature change to be ignored. Is the melting of the ice reversible or irreversible? Explain, using simple physical reasoning without resorting to any equations.

A box is separated by a partition into two parts of equal volume. The left side of the box contains $500$ molecules of nitrogen gas; the right side contains $100$ molecules of oxygen gas. The two gases are at the same temperature. The partition is punctured, and equilibrium is eventually attained. Assume that the volume of the box is large enough for each gas to undergo a free expansion and not change temperature. On average, how many molecules of each type will there be in either half of the box?