JEE PYQ: Thermodynamics Question 45
Question 45 - 2019 (12 Jan Shift 2)
A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is $K_1$ and that of the outer cylinder is $K_2$. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is:
(1) $\frac{K_1 + K_2}{2}$
(2) $K_1 + K_2$
(3) $\frac{2K_1 + 3K_2}{5}$
(4) $\frac{K_1 + 3K_2}{4}$
Show Answer
Answer: (4)
Solution
Effective thermal conductivity of system:
$K_{\text{eq}} = \frac{K_1 A_1 + K_2 A_2}{A_1 + A_2}$
$= \frac{K_1 \pi R^2 + K_2[\pi(2R)^2 - \pi R^2]}{\pi(2R)^2}$
$= \frac{K_1(\pi R^2) + K_2(3\pi R^2)}{4\pi R^2} = \frac{K_1 + 3K_2}{4}$
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