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?

(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

(a) the water,

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

(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, the surroundings, and the universe as a whole.

(d) How would your answers differ if the process were irreversible?

(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 (b) the surroundings.

(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 (c) 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

(II) 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.

(a) 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

(a) 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.

(a) Make an estimate

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

(b) use the integral ∆S = ∫ dQ / T.

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

(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..

(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

(b) the total change in entropy as a result of the mixing process (use ∆S = ∫ dQ / T ).

(II) 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.

(b) Determine the change in entropy of the gas for each process by integration.

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.

An aluminum can, with negligible heat capacity, is filled with 450 g of water at 0°C and then is brought into thermal contact with a similar can filled with 450 g of water at 50°C. Find the change in entropy of the system if no heat is allowed to exchange with the surroundings. Use ∆S = ∫ dQ / T .

(II) Why would you expect the total entropy change in a Carnot cycle to be zero? (b) Do a calculation to show that it is zero.

(II) A real heat engine working between heat reservoirs at 970 K and 650 K produces 550 J of work per cycle for a heat input of 2500 J.

(a) Compare the efficiency of this real engine to that of an ideal (Carnot) engine.