23. The Second Law of Thermodynamics

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 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.

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 sophomore with nothing better to do adds heat to $0.350$ kg of ice at $0.0$°C until it is all melted. What is the change in entropy of the water?

A $4.50$-kg block of ice at $0.00$°C falls into the ocean and melts. The average temperature of the ocean is $3.50$°C, including all the deep water. By how much does the change of this ice to water at $3.50$°C alter the entropy of the world? Does the entropy increase or decrease? (Hint: Do you think that the ocean temperature will change appreciably as the ice melts?)

A 75 g ice cube at 0℃ is placed on a very large table at 20℃. You can assume that the temperature of the table does not change. As the ice cube melts and then comes to thermal equilibrium, what are the entropy changes of (a) the water, (b) the table, and (c) the universe?

What is the entropy change of the nitrogen if 250 mL of liquid nitrogen boils away and then warms to 20℃ at constant pressure? The density of liquid nitrogen is 810 kg/m³.

2.0 mol of helium at 280℃ undergo an isobaric process in which the helium entropy increases by 35 J/K. What is the final temperature of the gas?

A thin partition divides a container of volume V into two parts. One side contains n_A moles of gas A in a fraction f_A of the container; that is, V_A = f_AV. The other side contains nB moles of a different gas B at the same temperature in a fraction f_B of the container. The partition is removed, allowing the gases to mix. Find an expression for the change of entropy. This is called the entropy of mixing.

A 2.0 mol sample of oxygen gas in a rigid, 15 L container is slowly cooled from 250℃ to 50℃ by being in thermal contact with a large bath of 50℃ water. What is the entropy change of (a) the gas and (b) the universe?

(II) If 0.45 kg of water at 100°C is changed by a reversible process to steam at 100°C, determine the change in entropy of the water.

What is the change in entropy of 280 g of steam at 100°C when it is condensed to water at 100°C?

(II) An aluminum rod conducts 8.25 cal/s from a heat source maintained at 225°C to a large body of water at 22°C. Calculate the rate at which entropy increases in this process.

If 0.45 kg of water at 100°C is changed by a reversible process to steam at 100°C, determine the change in entropy of the water, the surroundings, and the universe as a whole. How would your answers differ if the process were irreversible?