Question

Three cylindrical rods $A,B$ and $C$ of equal lengths and equal diameters are joined in series as shown in the figure. Their thermal conductivities are $2k,k$ and $0.5k$ respectively. In the steady state, the free ends of rods $A$ and $C$ are at 100${}^o$C and 0${}^o$C respectively. Neglect loss of heat from the curved surfaces of rods.

The equivalent thermal conductivity of the combination is :

• A. $\frac{7k}{3}$
• B. $\frac{2k}{7}$
• C. $\frac{5k}{3}$
• D. $\frac{3k}{5}$

Answer 1

The correct option is B $\frac{2k}{7}$

Here all the dimensions are same so we can find equivalent thermal conductivity as follow:

$\Rightarrow \frac{1}{K_{EQUIVALENT}}=\frac{1}{K_A}+\frac{1}{K_B}+\frac{1}{K_C}=\frac{1}{2k}+\frac{1}{k}+\frac{1}{0.5k}=\frac{3.5}{k}$

$\Rightarrow K_{EQUIVALENT}=\frac{2k}{7}$