Thermal Properties of Matter - Result Question 12
12. Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be :
[2017]
(a) $\frac{3(K_1+K_2)}{2}$
(b) $K_1+K_2$
(c) $2(K_1+K_2)$
(d) $\frac{K_1+K_2}{2}$
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Answer:
Correct Answer: 12. (d)
Solution:
- (d) Equivalent thermal conductivity of the composite rod in parallel combination will be,
$ \begin{aligned} K= & \frac{K_1 A(T_1-T_2)}{d}+\frac{K_2 A(T_1-T_2)}{d} \\ & \frac{K _{E Q. 2 A(T_1-T_2)}{d}=\frac{A(T_1-T_2)}{d}[K_1+K_2] \end{aligned} $
Hence equivalent thermal conductivities for two rods of equal area is given by
$ K _{E Q}=\frac{k_1+k_2}{2} $
