Question

Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity $k$ and the other $2k$. The temperature difference between the ends along the $x$-axis is the same in both the configurations. It takes $9$ s to transport a certain amount of heat from the hot end to the cold end in the configuration $I$. The time to transport the same amount of heat in the configuration $II$ is :

• A. 2.0 s
• B. 3.0 s
• C. 4.5 s
• D. 6.0 s

Answer 1

Answer: (A)

$R_1=\frac{L}{\kappa A}+\frac{L}{2\kappa A}=\frac{3L}{2\kappa A}$
$\frac{1}{R_2}=\frac{1}{\left(\frac{L}{KA}\right)}+\frac{1}{\left(\frac{L}{2\kappa A}\right)}=\frac{3\kappa A}{L}$
$R_2=\frac{L}{3\kappa A}$
$\Delta Q_1=\Delta Q_2$
$\frac{\Delta T}{R_1}{t}_1=\frac{\Delta T}{R_2}{t}_2$
$\Rightarrow t_2=\frac{R_2}{R_1}{t}_1$
$=2\sec$