The data listed below are claimed for a power cycle operating between hot and cold reservoirs at $1500$K an $450$K$,$ respectively. For each case, determine whether cycle operates reversibly, irreversibly, or is impossible. $($a$)$ QH$=600$ kJ$,$ W$=300$ kJ$,$ QL$=300$ kJ $($b$)$ QH$=400$ kJ$,$ W$=280$ kJ$,$ QL$=120$ kJ$($c$)$ QH$=700$ kJ$,$ W$=300$ kJ$,$ QL$=500$ kJ $($d$)$ QH$=800$ kJ$,$ W$=600$ kJ$,$ QL$=200$ kJ