Solution Found!
A house has well-insulated walls 17.5 cm thick (assume conductivity of air) and area 410
Chapter 14, Problem 56GP(choose chapter or problem)
Problem 56GP
A house has well-insulated walls 17.5 cm thick (assume conductivity of air) and area 410 m2, a roof of wood 6.5 cm thick and area 280 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 its inside temperature at 23°C if the outside temperature is –10°C. (b) If the house is initially at 10°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 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°.
Questions & Answers
QUESTION:
Problem 56GP
A house has well-insulated walls 17.5 cm thick (assume conductivity of air) and area 410 m2, a roof of wood 6.5 cm thick and area 280 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 its inside temperature at 23°C if the outside temperature is –10°C. (b) If the house is initially at 10°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 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°.
ANSWER:
Solution 56GP
Part (a)
Step 1 of 6:
A well-insulated house lost its heat by conduction. We are going to calculate the rate at which the heat has to be supplied to maintain the temperature inside the house at 23°C if the outside temperature is -10°C.
The given data are
The temperature inside the house T1 = 23°C
The outside temperature T2 = -10°C
The area of the wall A1 = 410 m2
The thickness of the wall l1 = 17.5 cm = 0.175 m
The area of the roof A2 = 280 m2
The thickness of the roof l2 = 6.5 cm = 0.065 m
The area of the window A3 = 33 m2
The thickness of the window l3 = 0.65 cm = 0.0065 m
The conductivity of wall k1 = 0.023 J/s.m.°C
The conductivity of roof k2 = 0.12 J/s.m.°C
The conductivity of window k3 = 0.84 J/s.m.°C