23. The Second Law of Thermodynamics

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 surroundings.

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.

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

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?

Two 1100-kg cars are traveling 75 km/h in opposite directions when they collide and are brought to rest. Estimate the change in entropy of the universe as a result of this collision. Assume T = 20°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.

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) The temperature of 1.6 mol of an ideal diatomic gas goes from 25°C to 55°C at a constant volume. What is the change in entropy? Use ∆S = ∫ dQ / T.

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?)

(II) A 110-g insulated aluminum cup at 35°C is filled with 150 g of water at 45°C. After a few minutes, equilibrium is reached. Determine the total change in entropy as a result of the mixing process (use ∆S = ∫ dQ / T ).

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.

Calculate the change in entropy of 1.00 kg of water when it is heated from 0°C to 85°C. Use the integral ∆S = ∫ dQ / T.