For a cryogenic experiment, heat should be removed from a space at 75 K to a reservoir at180 K. A heat pump is designed to use nitrogen and methane in a cascade arrangement (see Fig. 9.28), where the high temperature of the nitrogen condensation is 10 K higher than the low-temperature evaporation of the methane. The two other phase changes take place at the listed reservoir temperatures. Find the saturation temperature in the heat exchanger between the two cycles that gives the best COP for the overall system.