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

Answer:

[/tex] 408.8[/tex]

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

$Q = \frac{kA \Delta T}{t}$

$Q = \frac{(0.141) (13.4) (34.4)}{0.159}\\Q = 408.8$ W