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Chapter 3: Problem 226

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) \(0.143 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\) (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

Expert verified
Answer: (a) 0.143 m²K/W

Step by step solution

01

Convert wall thickness to meters

As the wall thickness is given in centimeters, we should convert it to meters: $$ 10\,\text{cm} \times \frac{1\,\text{m}}{100\,\text{cm}} = 0.1\,\text{m} $$
02

Use the formula to find thermal resistance per unit area

We will use the formula R/A = L/k. In our case, L = 0.1 m and k = 0.7 W/mK. $$ \frac{R}{A} = \frac{0.1\,\text{m}}{0.7\,\text{W/mK}} = 0.1428... \,\text{m}^2 \cdot \text{K/W} $$
03

Compare the result with the options

Our result, 0.1428 m²K/W, is closest to option (a) 0.143 m²K/W. So the correct answer is: (a) \(0.143 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}\)

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Most popular questions from this chapter

Hot water at an average temperature of \(70^{\circ} \mathrm{C}\) is flowing through a \(15-\mathrm{m}\) section of a cast iron pipe \((k=52 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) whose inner and outer diameters are \(4 \mathrm{~cm}\) and \(4.6 \mathrm{~cm}\), respectively. The outer surface of the pipe, whose emissivity is \(0.7\), is exposed to the cold air at \(10^{\circ} \mathrm{C}\) in the basement, with a heat transfer coefficient of \(15 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The heat transfer coefficient at the inner surface of the pipe is \(120 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Taking the walls of the basement to be at \(10^{\circ} \mathrm{C}\) also, determine the rate of heat loss from the hot water. Also, determine the average velocity of the water in the pipe if the temperature of the water drops by \(3^{\circ} \mathrm{C}\) as it passes through the basement.

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