The roof of a house consists of a 15-cm-thick concrete slab (k = 2 W/m · °C) that is 15 m wide and 20 m long. The emissivity of the outer surface of the roof is 0.9, and the convection heat transfer coefficient on that surface is estimated to be 15 W/m² . °C. The inner surface of the roof is maintained at 15°C. On a clear winter night, the am- bient air is reported to be at 10°C while the night sky tempera- ture for radiation heat transfer is 255 K. Considering both radiation and convection heat transfer, determine the outer sur- face temperature and the rate of heat transfer through the roof. If the house is heated by a furnace burning natural gas with an efficiency of 85 percent, and the unit cost of natural gas is $0.60/therm (1 therm = 105,500 kJ of energy content), de- termine the money lost through the roof that night during a 14-hour period.