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Q.

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 thermal conductivity of rod A)

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a

$\frac{2}{3} K_{A}$

b

3K_A

c

2K_A

d

$\frac{1}{3} K_{A}$

answer is A.

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Detailed Solution

Given, $K_{B} = K_{A} / 2$

and $K_{B} = 3 K_{C}$

$∴ K_{C} = K_{A} / 6$

$A B C$

Rods are in series form, so

$\frac{L}{K} = \frac{l_{1}}{K_{A}} + \frac{l_{2}}{K_{B}} + \frac{l_{3}}{K_{C}}$

$\frac{3 l}{K} = \frac{l}{K_{A}} + \frac{l}{K_{A} / 2} + \frac{l}{K_{A} / 6}$ $(∵ l = l_{1} = l_{2} = l_{3})$

or $\frac{3 l}{K} = \frac{9 l}{K_{A}} or K = \frac{K_{A}}{3}$

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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 (KA is the thermal conductivity of rod A)