Question

A plane brick wall \((k=0.7 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) is $10 \mathrm{~cm}$ thick. The thermal resistance of this wall per unit of wall area is (a) \(0.143 \mathrm{~m}^{2}, \mathrm{~K} / \mathrm{W}\) (b) \(0.250 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\) (c) \(0.327 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\) (d) \(0.448 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\) (e) \(0.524 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\)

Short answer

Question: A brick wall with a thermal conductivity of 0.7 W/m·K and a thickness of 10 cm has a thermal resistance per unit area equal to: (a) 0.143 m²·K/W (b) 1.43 m²·K/W (c) 14.3 m²·K/W (d) 0.0143 m²·K/W Answer: (a) 0.143 m²·K/W

Step-by-step solution

Write the formula for thermal resistance.

The formula for thermal resistance (R) for a plane wall is given by: R = L / kA where L is the thickness of the wall, k is the thermal conductivity and A is the area of the wall. Since we need to find the thermal resistance per unit area, we can remove the area 'A' from the equation. So now our formula becomes: R = L / k

Substitute given values.

Now, let's substitute the given values in the formula: L = 10 cm = 0.1 m (converting cm to meters) k = 0.7 W/m·K R = (0.1 m) / (0.7 W/m·K)

Calculate the thermal resistance.

Now, let's calculate the thermal resistance: R = 0.1 / 0.7 = 0.1428571... m²·K/W

Choose the correct answer.

By comparing our calculated value to the given options, we can conclude that the closest value is the following: (a) 0.143 m²·K/W So the correct answer is (a) 0.143 m²·K/W.