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?

Question

Quizplus · Accepted Answer

We can use the formula for rate of heat conduction through a material:

Q/t = kA(T1-T2)/d

Where:
Q/t = rate of heat conduction (what we want to find)
k = thermal conductivity of the material (given as 0.141 W/(m · C°))
A = area of the material (given as 13.4 m^2)
T1 = temperature on one side of the material (18.0 °C inside the cabin)
T2 = temperature on the other side of the material (-16.4 °C in the crawl space)
d = thickness of the material (given as 0.159 m)

Plugging in the values and solving for Q/t, we get:

Q/t = (0.141 W/(m · C°) * 13.4 m^2 * (18.0 °C - (-16.4 °C))) / 0.159 m
Q/t = 408 J/s

So the rate of heat conduction through the wooden floor is 408 J/s. Therefore, the answer is D)408 J/s.

A Cabin Has a 0