A brick wall of 20 cm thickness has thermal conductivity of 0.7 W
| A brick wall of 20 cm thickness has thermal conductivity of 0.7 W/m.K. An insulation of thermal conductivity 0.2 W/m.K is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. Which of the following are the INCORRECT statements?
A. The required thickness of the insulation is 1.714 cm
B. The required thickness of the insulation is 34.56 cm
C. The required thickness of the insulation is 17.14 cm
D. The required thickness of the insulation is 3.456 cm
Please scroll down to see the correct answer and solution guide.
Right Answer is:
SOLUTION
Explanation:
\({{q}_{1}}=\frac{{{T}_{1}}-{{T}_{2}}}{\left( \frac{0.2}{0.7} \right)}\)
\({{q}_{2}}=\frac{{{T}_{1}}-{{T}_{2}}}{\frac{0.2}{0.7}+\frac{t}{0.2}}\)
q2 = 0.25 q1
\(\frac{{{T}_{1}}-{{T}_{2}}}{\frac{0.2}{0.7}+\frac{t}{0.2}}=0.25\times \frac{{{T}_{1}}-{{T}_{2}}}{\left( \frac{0.2}{0.7} \right)}\)
\(\frac{2}{7}=0.25\times \left( \frac{2}{7}+\frac{t}{0.2} \right)\)
\(\frac{8}{7}=\frac{2}{7}+\frac{t}{0.2}\)
⇒t = 0.1714 m
∴ t = 17.14 cm
