The First Law of Thermodynamics

[rico22]

Homework Statement

The average thermal conductivity of the walls (including the windows) and roof of a house is 0.480 W/m · °C, and their average thickness is 24.7 cm. The house is heated with natural gas having a heat of combustion (that is, the energy provided per cubic meter of gas burned) of 9 300 kcal/m3. How many cubic meters of gas must be burned each day to maintain an inside temperature of 23.5°C if the outside temperature is 0.0°C? Disregard radiation and the energy lost by heat through the ground.

the Side walls are 5m x 8 m and the front and back walls are 5m x 10 m respectively. The roof has an incline of 37 degrees between the roof and the side of the house.

Homework Equations

rate of heat transfer P = (k(thermal conductivity)A ΔT)/Δx

The Attempt at a Solution

I tried finding the rate of heat transfer for the house. side wall, front wall and the roof and I added them up. then I found how many total joules were transferred for the day as this give me Joules/ sec. After I got this I converted it into cal by multiplying it by .239 and then kcal. finally I divided the total amount of kcal by the 9300 kcal/m³ given. I just want to know if I am on the right track or am I way off? Thanks in advance.

 

[haruspex]

Yes, that's the right procedure. For the first step, I would have just added the areas rather than calculating the rates separately then adding them up. Can't check the details without seeing your working.

 

[rico22]

Thanks for the reply