$5\mathrm{.}37$ A power cycle operates between hot and cold reservoirs at $600$ K and $300$ K$,$ respectively. At steady state the cycle develops a power output of $0\mathrm{.}45$ MW while receiving energy by heat transfer from the hot reservoir at the rate of $1$ MW$.($a$)$ Determine the thermal efficiency and the rate at which energy is rejected by heat transfer to the cold reservoir, in MW$.($b$)$ Compare the results of part $($a$)$ with those of a reversible power cycle operating between these reservoirs and receiving the same rate of heat transfer from the hot reservoir.