Question

A cabin has a 0.159-m thick wooden floor [k = 0.141 W/(m · C°)] with an area of 13.4 m2. A roaring fire keeps the interior of the cabin at a comfortable 18.0 °C while the air temperature in the crawl space below the cabin is –16.4°C. What is the rate of heat conduction through the wooden floor?

Answer 1

[/tex] 408.8[/tex]

Step-by-step explanation:

`t` = thickness of the floor = 0.159 m

`k` = thermal conductivity of wooden floor = 0.141 Wm⁻¹ ⁰C⁻¹

`T_(i)` = Temperature of the interior of the cabin = 18.0 ⁰C

`T_(o)` = Temperature of the air below the cabin = - 16.4 ⁰C

Difference in temperature is given as

`\Delta T` = Difference in temperature =
`T_(i) - T_(o) = 18 - (- 16.4) = 34.4`⁰C

`A` = Area of the floor = 13.4 m²

`Q` = Rate of heat conduction

Rate of heat conduction is given as

`Q = (kA \Delta T)/(t)`

`Q = ((0.141) (13.4) (34.4))/(0.159)\\Q = 408.8` W