Suppose you have an electric hot water heater for your house which is an aluminum cylinder which has a 0.56 m radius and is 1.8 m high. The walls are 1.0 cm thick. The thermal conductivity of Aluminum is 217 W/(m K). Assume that the temperature of the hot water inside the hot water heater is kept at a constant 90 C, and the external temperature is 27 C.
A) Assume you pay $0.10 per kW-hour for electricity. How much would it cost just to keep the hot water inside the heater for one week? The Joules are 6.87 *10^12.
B) Suppose that you wrap the hot water heater on all sides with a 10 cm thick blanket of fiberglass insulation which has a thermal conductivity of 0.04 W/(m K). Assume the inner surface of the fiberglass insulation is at 90 C and the outer surface is at 27 C, and the total surface area is still what you calculated in part A.
C) Assume you pay $0.10 per kW-hour for electricity. How much would it cost just to keep the hot water inside the fiberglass-wrapped heater for one week?