David wants to set up a solar thermal water heating system at his house The normal temperature of cold tap water at his house is 65F and David's household uses a total of 200 gallons of hot water at a starting temperature at Joe's hot water tank of 112F every day. Assuming no heat losses, calculate much energy (in Joules) is required to provide the David household with hot water every day If David uses an electric hot water heater that uses a resistive heating element to heat water in David's hot water tank, and there are no heat losses from the tank, estimate David's annual hot water heating bill assuming an electricity cost of $0.20 per kilowatt hour. David designs a solar water heating system for his roof. The heating system consists of a flat aluminum plate with pipes running through it, and thick thermal insulation on the back to prevent conductive heat loss. The aluminum plate is black and has a solar reflectance of 0.05, and it has an infrared emissivity of 0.7. If the average flux of solar radiation when the sun is directly overhead at Joe's house is 1000 W/m^2 , and the sun is typically 45 degrees above the horizon at David's house during the day, calculate the typical radiative equilibrium temperature of the flat aluminum plate assuming that Joe mounts it horizontally on his roof. Provide your answer in degrees Kevin and degrees Fahrenheit. Water enters the solar heating plate at 65F, and exits the solar heating plate at 112F, which cools down the plate to an overall average temperature of approximately 150F. Estimate the surface area of plate (in square meters) that would be required to heat the water for David's house assuming that the flow rate of water through the plate is 200 gallons in 6 hours, and that the average sun angle is 45 degrees, and that the difference between the absorbed solar energy and emitted thermal energy by the plate goes to heating the water that is flowing through the plate. Hint: The plate heats up 200 gallons of water from a temperature of 65F to 112F in 6 hours.