Question

$1.56\times {10}^{5}J$ of heat is conducted through a $2m^2$ wall of $12cm$ thickness in $1hr$. Temperature difference between the two sides of the wall is ${20}^{o}C$. The thermal conductivity of the material of the wall is (in $W{m}^{-1}{K}^{-1}$) :

• A. $0.11$
• B. $0.13$
• C. $0.15$
• D. $1.2$

Answer 1

Answer: (B)

$0.13$

Given: $A=2m^2$, $l=12cm=0.12$ $m$, $\Delta T={20}^{o}C=20K$

Rate of heat flowing through the wall, $\frac{dQ}{dt}=\frac{1.56\times {10}^{5}J}{1h}=\frac{1.56\times 105J}{3600s}=43.33$ $J{s}^{-1}$

Using $\frac{dQ}{dt}=\frac{KA\Delta T}{l}$, where $K$ is the thermal conductivity

$\Rightarrow 43.33=\frac{K\times 2\times 20}{0.12}$

$\Rightarrow K=0.13$ $W{m}^{-1}{K}^{-1}$