Chapter 19, Problem 76GP

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 280 m², and uncovered windows 0.65 cm thick and total area 33m². (a) Assuming that heat is lost only by conduction, calculate the rate at which heat must he supplied to this house to maintain its inside temperature at 23°C if the outside temperature is −15°C. (b) If the house is initially at 12°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 750m³ (c) If natural gas costs $0.080 per kilogram and its heat of combustion is 5.4 × 10⁷ J/kg, how much 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°.