Question

Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$ and cross sectional areas $A_1$ and $A_ 2$ respectively. If the rate of heat conduction in 1 is four times that in 2, then :

• A. $K _1A_1 = 4K_2A_2$
• B. $K_1A_1= 2K_2A_2$
• C. $4K_1A_1= K_2A_2$
• D. $K_1A_1= K_2A_2$

Answer 1

Answer: (A)

$K _1A_1 = 4K_2A_2$

Answer 2

(a): Let L be length of each rod.
Rate of heat flow in rod 1 for the temperature
difference $\Delta T$ is
$H_1 = \frac{ K_1A_1 \Delta T }{ L}$
Rate of heat flow in rod 2 for the same difference
$\Delta T$ is
$H_2 = \frac{ K _2A_2 \Delta T }{ L}$
As per question
$H_1 = 4H_2$
$\frac{K_1A_1 \Delta T }{ L } = 4 \frac{K_2A_2 \Delta T }{ L }$
$K_1A_1= 4K_2A_2$