Two reversible heat pump cycles operate in series. The first cycle receives energy by heat transfer from a cold reservoir at 250 K and rejects energy by heat transfer to a reservoir at an intermediate temperature T greater than 250 K. The second cycle receives energy by heat transfer from the reservoir at temperature T and rejects energy by heat transfer to a higher- temperature reservoir at 1440 K. If the heat pump cycles have the same coefficient of performance, determine (a) T, in K, and (b) the value of each coefficient of performance.