A geothermal resource outputs saturated (liquid) water at 250 ^◦C (as in Example 32.5). Consider two alternative ways to use this resource to deliver space heating at T = 20 ^◦C. First, the hot water is circulated through a heat exchanger that transfers its thermal energy with 90% (1st law) efficiency to the space to be heated. Second, the geothermal resource is used to generate electric power at 13% (1st law) efficiency. The electric power in turn runs a heat pump with a 2nd law efficiency of 33% that operates between T and an outside temperature T₀. Further, the waste heat from the geothermal power plant in the form of saturated water at 50 ^◦C is circulated through a heat exchanger at 90%(1st law) efficiency to provide additional space heating. What is the minimum ambient temperature T₀ for which the second system outperforms the first? You will need to look up the specific enthalpy of saturated (liquid) water at various temperatures.