The steady state data listed below are claimed for a power cycle operating between hot and cold reservoirs at $1400$K and $400$K respectively. For each case, evaluate the net power developed in the cycle, in kW$,$ and the thermal efficiency. Also in each case, apply Eq$.5\mathrm{.}13$ on a time$-$rate basis to determine whether the cycle operates reversibly, operates irreversibly, or is impossible.

$($a$)$ QH $=500$ kW$,$ Qc $=400$ kW

$($b$)$ QH $=500$ kW$,$ Qc $=0$ kW

$($a$)$ QH $=500$ kW$,$ Qc $=200$ kW