Question

Three rods $A,B$ and $C$ have the same dimension. Their thermal conductivities are $k_A,k_B$ and $k_C$. They are placed individually, with their ends kept at the same temperature difference. The rate of heat flow through $C$ is equal to the rate of combined heat flow through $A$ and $B$. $k_C$ must be equal to:

• A. $k_A+k_B$
• B. $\frac{k_A{k}_B}{k_A+k_B}$
• C. $\frac{1}{2}(k_A+k_B)$
• D. $2\frac{k_A{k}_B}{k_A+k_B}$

Answer 1

The correct option is A $k_A+k_B$

Given that three rod have same dimensions and kept their ends at same temperature differnce. If the rate of heat flow through C is equal to the rate of combined heat
flow through A and B
$\frac{k_c\times a\times (T_2-T_1)}{L}=\frac{k_a\times a\times (T_2-T_1)}{L}+\frac{k_b\times a\times (T_2-T_1)}{L}$
where $K$ is the effective thermal conductivity, $T_2-T_1$ is the temperature difference between the ends of three rods, $a$ is area and $L$ is the length
of the each rod
$\frac{k_c\times a}{L}=\frac{k_a\times a}{L}+\frac{k_b\times a}{L}$
$k_c=k_a+k_b$