Consider the reversible Carnot cycle shown in Figure 5.2 with 1.25 mol of an ideal gas with C_V= 5/2R as the working substance. The initial isothermal expansion occurs at the hot reservoir temperature of T_hot= 740.K from an initial volume of 3.75 L (V_a) to a volume of 12.8 L (V_b). The system then undergoes an adiabatic expansion until the temperature falls to T_cold= 310.K. The system then undergoes an isothermal compression and a subsequent adiabatic compression until the initial state described by T_a= 740.K and V_a= 3.75 L is reached. 

a. Calculate V_c and V_d .

b. The gas is heated to 675 K at a constant volume corresponding to the initial volume.

c. The gas undergoes a reversible isothermal expansion at 310. K until the pressure is one third of its initial value.

Figure 5.2

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Isothermal expansion Pa Adiabatic cold compression Adiabatic expansion hot Isothermal compression Pg- hot Pc Va Va Vo Vc Volume Pressure