Question

Three rods A, B and C have the same dimensions. Their thermal conductivities are k_A, k_B, and k_Crespectively. A and B are placed end to end, with their free ends kept at certain temperature difference. C is placed separately with its ends kept at same temperature difference. The two arrangements conduct heat at the same rate. 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. $\frac{2k_{A}k_{B}}{k_{A} + k_{B}}$

Answer 1

Answer: (B)

$\frac{k_{A}k_{B}}{k_{A} + k_{B}}$

Answer 2

$\frac{T_{1}–T_{2}}{\frac{L}{k_{A}A} + \frac{L}{k_{B}A}}$ = $\frac{T_{1}–T_{2}}{\frac{L}{k_{C}A}}$

$\frac{k_{A}k_{B}}{k_{A} + k_{B}}$ = k_C