A house has well-insulated walls 19.0 cm thick (assume conductivity of air) and

Question

A house has well-insulated walls 19.0 cm thick (assume conductivity of air) and area 391 m^2, a roof of wood 6.72 cm thick and area 269 m^2, and uncovered windows 0.660 cm thick and total area 32.2 m^2. 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 21.7 degree C if the outside temperature is -11.5 degree C. If the house is initially at 11.1 degree C, estimate how much heat must be supplied to raise the temperature to 21.7 degree C within 31.4 min. Assume that only the air needs to be heated and that its volume is 800 m^3. Take the specific heat of air to be 0.24 kcal/(kg middot C degree). If natural gas costs $0.084 per kilogram and its heat of combustion is 5.15 times 10^7 J/kg, how much is the monthly cost (in $) maintain the house at a temperature of 21.7 degree C for 24.0 hr each day assuming 90.7 percent of the heat produced is used to heat the house? (Do not enter units)

Explanation / Answer

Q/t = KA*dT/dx

Q/t = [k_wall * A_wall/0.19m + k_roof*A_roof/0.0672 + k_uw*A_uw/6.6x10^3m ] *dT

dT = 33.2

k_wall = heat conduction = 0.023

k_roof= 0.12

k_uw = 0.84

Q/t = 153578.85 J

part b )

Q = mc*dT + Q*condition

m = density * volume

air density = 1.29 kg/m^3

volume = 800

.24 kcal/kg*C = 1004.64 J/kg-C

Qconditio = Q/t * t

t = 31.4 min = 1884 s

Q= 3 x 10^8 J

part c )

0.907Qgas = Q/t * time

time = 30 * 86400 = 2592000 s

Qgas = 4.389 x 10^11 J

cost for 4.389 x 10^11 J

cost = 4.389 x 10^11 * 0.084 / 5.15 x 10^7

cost = 715.865

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