How do I determine the maximum theoretical coefficient of performance for a heat pump operating at steady state between a dwelling at 70 deg F and a pond at 40 deg F?

How do I determine the maximum theoretical coefficient of performance for a heat pump operating at steady state between a dwelling at 70 deg F and a pond at 40 deg F? For the dwelling, if heat transfer through the walls and roof is 6.5x10^5 Btu per day, how would I determine the minimum theoretical power, in hp, to drive a heat pump operating at steady state between the dwelling at 70 deg F and a pond at 40 deg F?

Water is the working fluid in an ideal Rankine cycle.

Water is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at 18 MPa. The condenser pressure is 6 kPa. How do I determine the quality of the fluid at the turbine exit, and the heat transfer to the steam passing through the boiler in kJ per kg of steam flowing. The enthalpy of the steam entering the turbine is 2509.1 kJ/kg and of the steam entering the pump is 151.53 kJ/kg.

At the beginning of a compression process of an air-standard Otto cycle

At the beginning of a compression process of an air-standard Otto cycle, p1 = 1 bar, T1 = 290 K, V1 = 400 cm^3. The maximum temperature in the cycle is 2200 K and the compression ratio is 8. How do I determine the mass of air contained in the system, in kg, and the heat addition, in kJ? The internal energy at the end of the isentropic compression is 475.11 kJ/kg.

A flash of lightning is sighted and 3 seconds later thunder is heard.

A flash of lightning is sighted and 3 seconds later thunder is heard. Approximately how far away ws the lightning strike, in meters?

A vapor-compression heat pump system uses R-134a as the working fluid.

A vapor-compression heat pump system uses R-134a as the working fluid. The refrigerant enters the compressor at 0.24 Mpa, 0 degrees Celsius, with a volumetric flow rate of 0.6m^3/min. The compression process is adiabatic to 0.9 MPa, 60 degrees Celsius, and saturated liquid exits the condenser at 0.9 MPa. Find the following: a.) The power input to the compressor, in kW. b.) The heating capacity of the system in kW (Qout) c.) The coefficient of performance d.) The compressor's isentropic efficiency.