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

Answer 1

Answer: (A)

$2.0s$

$R_1=\frac{L}{KA}+\frac{L}{2KA}=\frac{3L}{2KA}$

$\frac{1}{R_2}=\frac{1}{\left(\frac{L}{KA}\right)}+\frac{1}{\left(\frac{L}{2KA}\right)}=\frac{3KA}{L}$

$R_2=\frac{L}{3KA}$

$\Delta Q_1=\Delta Q_2$

$\frac{\Delta T}{R_1}{t}_1=\frac{\Delta T}{R_2}{t}_2$

$\Rightarrow t_2=\frac{R_2}{R_1}{t}_1=2sec$