23. The Second Law of Thermodynamics

3 moles of an ideal gas are compressed isothermally at 20°C. During this compression, 1850 J of work is done on the gas. What is the change of entropy of the gas?

You have a block of ice at 0°C. Heat is added to the ice, causing an increase in entropy of 120J/K. How much ice melts into water in this process?

A non-Carnot heat engine operates between a hot reservoir at 610K and a cold reservoir at 320K. In a cycle, it takes in 6400 J of heat and does 2200 J of work. What is the total change in entropy of the universe over the cycle?

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.