Consider a 2-m-high electric hot-water heater that has a diameter of 40 cm and maintains the hot water at 55°c. the tank is located in a small room whose average temperature is 27°c, and the heat transfer coefficients on the inner surface of the heater is 50 w/(m2 *°c), respectively. the tank is placed in another 46-cm-diameter sheet metal tank of negligible thickness, and the space between the two tanks is filled with foam insulation (k = 0.03 w/(m*°c). the heat transfer coefficient of the outer surface of the whole unit is 12 w/(m2 *°c). the thermal resistances of the water tank and the outer thin sheet metal shell are very small and can be neglected. the price of electricity if $0.08/kwh, and the home owner pays $280 a year for water heating. (a) determine the fraction of the hot-water energy cost of this household that is due to to the heat loss form the tank. hot water tank insulation kits consisting of 3-cm-thick fiberglass insulation (k = 0.035 w/m oc) large enough to wrap the entire tank are available in the market for about $30. if such an insulation is installed on this water tank by the home owner himself, how long will it take for this additional insulation to pay for itself?