23. The Second Law of Thermodynamics

(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 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. 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.

Why would you expect the total entropy change in a Carnot cycle to be zero? 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. Compare the efficiency of this real engine to that of an ideal (Carnot) engine.