Question

Three identical rods $A, B$ and $C$ are placed end to end. A temperature difference is maintained between the free ends of $A$ and $C$. The thermal conductivity of $B$ is thrice that of C and half of that of A The effective thermal conductivity of the system will be
$(k_{A}$ is the therm al conductivity of rod A)

• A. $\frac {1}{3}K_A$
• B. $3\,K_A$
• C. $2 \,K_A$
• D. $\frac {2}{3}K_A$

Answer 1

Answer: (A)

Given, $K_{B}=K_{A} / 2,$
and $K_{B}=3 K_{C} $
$\therefore K_{C}=K_{A} / 6$
Rods are in series form so
$\frac{L}{K}=\frac{l_{1}}{K_{A}}+\frac{l_{2}}{K_{B}}+\frac{l_{3}}{K_{C}}$
$\left(\because l=l_{1}=l_{2}=l_{3}\right)$
$\frac{3 l}{K}=\frac{l}{K_{A}}+\frac{l}{K_{A} / 2}+\frac{l}{K_{A} / 6}$
or $\frac{3 l}{K}=\frac{9 l}{K_{A}}$
or $K=\frac{K_{A}}{3}$