1) Consider the reversible Carnot cycle shown in Figure 5.2 with 1 mol of an ideal gas with CV = 3/2R as the working substance. The initial isothermal expansion occurs at the hot reservoir temperature of Thot = 600ºC from an initial volume of 3.50 L (Va) to a volume of 10.0 L (Vb). The system then undergoes an adiabatic expansion until the temperature falls to Tcold = 150ºC. The system then undergoes an isothermal compression and a subsequent adiabatic compression until the initial state described by Ta = 600ºC and Va = 3.50 L is reached.

a) Calculate Vc and Vd. b) Calculate w for each step in the cycle and for the total cycle. c) Calculate ε and the amount of heat that is extracted from the hot reservoir to do 1.00 kJ of work in the surroundings.

2) One mole of an ideal gas with CV = 3/2R undergoes the transformations described in the following list from an initial state described by T = 300 K and P = 1.00 bar. Calculate q, w, ΔU, ΔH, and ΔS for each process. a. The gas is heated to 450 K at a constant external pressure of 1.00 bar. b. The gas is heated to 450 K at a constant volume corresponding to the initial volume. c. The gas undergoes a reversible isothermal expansion at 300 K until the pressure is half of its initial value.

3) One mole of an ideal gas with CV,m = 5/2R undergoes the transformations described in the following list from an initial state described by T = 250 K and P = 1.00 bar. Calculate q, w, ΔU, ΔH, and ΔS for each process.

a. The gas undergoes a reversible adiabatic expansion until the final pressure is half its initial value.

b. The gas undergoes an adiabatic expansion against a constant external pressure of 0.500 bar until the final pressure is half its initial value.

c. The gas undergoes an expansion against a constant external pressure of zero bar until the final pressure is equal to half of its initial value.