23. The Second Law of Thermodynamics

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?

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.

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 universe as a whole.

(II) 1.00 mole of nitrogen (N₂) gas and 1.00 mole of argon (Ar) gas are in separate, equal-sized, insulated containers at the same temperature. The containers are then connected and the gases (assumed ideal) allowed to mix. What is the change in entropy

(a) of the system

Two samples of an ideal gas are initially at the same temperature and pressure. They are each compressed reversibly from a volume V to volume V/2, one isothermally, the other adiabatically. In which sample is the final pressure greater?

(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 final temperature.

(II) Calculate the change in entropy of 1.00 kg of water when it is heated from 0°C to 85°C. Make an estimate.

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.

Why would you expect the total entropy change in a Carnot cycle to be zero?