Answer :
The thermal conductivity of the wall is approximately 126.33 W/(m·K).
Thermal conductivity represents the ability of a material to conduct heat. In this scenario, we can use Fourier's Law of Heat Conduction, which states that the rate of heat conduction through a material is directly proportional to the surface area, the temperature difference across the material, and inversely proportional to the thickness of the material.
Mathematically, it's represented as [tex]\( \frac{Q}{A} = k \frac{\Delta T}{d} \)[/tex], where [tex]\( Q \)[/tex] is the heat transferred per unit time, [tex]\( A \)[/tex] is the surface area, [tex]\( k \)[/tex] is the thermal conductivity, [tex]\( \Delta T \)[/tex] is the temperature difference, and [tex]\( d \)[/tex] is the thickness of the material.
Rearranging the formula to solve for thermal conductivity, we get [tex]\( k = \frac{Q \cdot d}{A \cdot \Delta T} \)[/tex]. Plugging in the given values: [tex]\( Q = 37.9 \)[/tex] W, [tex]\( A = 3.00 \)[/tex] m², [tex]\( \Delta T = 20.0 - 0.00 = 20.0 \)[/tex] °C, and [tex]\( d = 0.01 \)[/tex] m, we find [tex]\( k \approx \frac{37.9 \times 0.01}{3.00 \times 20.0} \approx 126.33 \)[/tex] W/(m·K).
Therefore, the thermal conductivity of the wall is approximately 126.33 W/(m·K).
