A small building 5 m wide by 7 m long by 3 m high (inside dimensions) is mounted on a flat concrete slab having a thickness of 15 cm. The walls of the building are constructed of concrete also, with a thickness of 7 cm. The inside of the building is used for cold storage at −20ºC and the outside of the building is exposed to ambient air at 30ºC, with a convection coefficient of 15 W/m2 · ºC. The inside convection coefficient for the building is estimated at 10W/m2 · ºC and the floor slab is in contact with earth having k = 1.8 W/m· ºC. The earth temperature may be assumed to be 15ºC. Calculate the heat gained by the building in the absence of any insulating material on the outside. Next, select two alternative insulation materials for the outside of the building from Table 2-1 and/or Table A-3. The insulation objective is to raise the outside surface temperature of the insulation to 26ºC for the ambient temperature of 30ºC. The refrigeration system operates in such a manner that 1 kW will produce 4000 kJ/hr of cooling, and electricity costs $0.085/kWh. Economics dictates that the insulation should pay for itself in a three-year period. What is the allowable cost per unit volume of insulation to accomplish this payback objective, for the two insulating materials selected? Suppose an outside surface temperature of 24ºC is chosen as the allowable value for the insulation. What would the allowable costs be for a three-year payback in this case? Make your own assumptions as to the annual hours of operation for the cooling system.