A concrete wall of a cold storage room measures 3.0 m high,5.0 m wide,and 20 cm thick.The inside wall is to be covered by a layer of wood in order to reduce the rate of thermal energy flow through the wall by 90 percent.The inner surface of the wooden wall is maintained at -10°C and the outer surface of the concrete wall is at 20°C.The thermal conductivities of concrete and wood are 0.80 W/m ∙ K (concrete)and 0.040 W/m ∙ K (wood).What should be the thickness of the layer of wood?

Question

Quizplus · Accepted Answer

First, we need to find the rate of energy flow through the current concrete wall without the wood layer.
We can use the formula:
Q/t = [kA (T1 - T2)] / d
where 
Q/t = rate of energy flow (in Watts)
k = thermal conductivity (in W/m ∙ K)
A = surface area (in m^2)
T1 - T2 = temperature difference (in K)
d = thickness (in m)

We can calculate Q/t as follows:
Q/t = [0.80 (5.0 x 3.0)] / 0.20 x (20 - (-10))
Q/t = 12.00 W

Now, we need to reduce this energy flow by 90 percent. This means the new rate of energy flow with the wood layer should be:
Q/t' = 0.10 x Q/t
Q/t' = 1.20 W

We can use the same formula as before to find the required thickness of the wood layer:
1.20 = [0.040 (5.0 x 3.0)] / d x (20 - (-10))
d = 0.09 m = 90 mm

Therefore, the thickness of the layer of wood should be 90 mm, which is option D.

A Concrete Wall of a Cold Storage Room Measures 3