Show that the two states specified in Probe 7.10 lie on an adiabatic curve. A cycle described by J. Willis and D. Kirwan, and called the "Sadly Cannot" cycle, is obtained by proceeding from the initial state to the final state along the straight line specified in Probe 7.10 and back to the initial state along the adiabatic curve. Calculate:

(a) The work done on the gas during the adiabatic process.

(b) The net work done in the cycle.

(c) The net heat transferred to the gas.

(d) The thermal efficiency of the cycle.

(e) The thermal efficiency of a Carnot cycle operating between a reservoir at the maximum temperature in the cycle and a reservoir at the minimum temperature in the cycle.