can you help me solve part b, c . show all work please. thank you PartB A house

Question

can you help me solve part b, c . show all work please.
thank you

PartB A house has well-insulated wals 15.0 cm thick (assume conductivity of air) and area 480 m2 a roof af wood 7.2 em thick and area 300 m2 and uncovered windows 0.80 cm thick and total area 32 m If the house is inialy at 15 C, essimabo how much heat must be supplied to raise the temperature to 20 C within 20 min. Assume that only the air needs to be heated and that its volume is 750 m. Take the specific hesat of air to be 0.24 kcal/kg-C Express your answer using two significant figures Ay x"?????.x x m x.io' usted Submit X Incorrect; Try Again; 5 attempts remaining

Explanation / Answer

given, well insulated house

thickness of walls, t = 0.15 m

A = 480 m^2

conductivity of air, ka = 0.0262 W/mK

roof, wooden Aw = 300 m^2

tw = 0.072 m

conductivity, kw = 0.2 W/m K

hence

B. Ti = 15 C

Q = ?

Tf = 20 C

time, t' = 20 min = 20*60 s = 1200 s

Tav = (Ti + Tf)/2 = 17.5 C

rate of heat dissipation = ka*A*dT/t + kw*Aw*dT/tw

dT = (Tav - To)

here To is temperature of the outside ( which is required)

hence

r = 917.1733333(17.5 - To)

hence

heat required

q = rho*V*c*(20 - 15) + r*t

hence

rho = 1.2 kg/m^3

V =750 m^3

c = 0.24 kcal/kg C

c = 1004.16 J/kg C

hence

q = 4518720 + 1100607.99996(17.5 - To) J

C. 1 kg natural gas = $0.08

1 kg = 5.4*10^7 J

hence

kg of fuel burnt = (4518720 + 1100607.99996(17.5 - To))/0.9*5.4*10^7

m = 0.09297777777 + 0.022646255143(17.5 - To) = 0.489287242776172 - 0.02264625514To

hence

cost = 0.08*m dollars

all we need is To in C

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