A house has well-insulated walls 19.5 cm thick (assume conductivity of air) and area 410 m2, a roof of wood 5.5 cm thick and area 250 m2, and uncovered windows 0.65 cm thick and total area 33 m2.

(a) Assuming that heat is lost only by conduction, calculate the rate at which heat must be supplied to this house to maintain it's inside temperature at 23°C if the outside temperature is - 15° C.

(b) If the house is initially at 15°C, estimate how much heat must be supplied to raise the temperature to 23°C within 30 min. Assume that only the air needs to be heated and that its volume is 750 m3.

(c) If natural gas costs $0.080 kg and its heat of combustion is 5.4 × 107 J/kg, what is the monthly cost to maintain the house as in part (a) for 24 h each day, assuming 90% of the heat produced is used to heat the house? Take the specific heat of air to be 0.24 kcal /kg ∙ C°.