A house has well-insulated walls 17.5 cm thick (assume conductivity of air) and

Question

A house has well-insulated walls 17.5 cm thick (assume conductivity of air) and area 406 m2, a roof of wood 6.5 cm thick and area 287 m2, and uncovered windows 0.65 cm thick and total area 32 m2. Take the specific heat of air to be 0.24 kcal/kg·C°.

(a) Assuming that the heat loss is only by conduction, calculate the rate at which heat must be supplied to this house to maintain its temperature at 23°C if the outside temperature is -10°C.
(Answer in kWatts)

(b) If the house is initially at 7°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.
(Answer in Joules)

(c) If natural gas costs $0.080 per kilogram and its heat of combustion is 5.4 * 10^7 J/kg, how much is the monthly cost to maintain the house as in part (a) for 24 h each day assuming 85 percent of the heat produced is used to heat the house?
(Answer in dollars/month)

Explanation / Answer

a) 155.7 kW b)2.28J c)$703

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