First slide

Conduction

Question

A metallic sphere having inner and outer radii ‘a’ and ‘b’ respectively has thermal conductivity $K = K_{0} / r^{2} (a \leq r \leq b)$ where $K_{0}$ is a constant. The thermal resistance between inner and outer surface is

Difficult

A

$\frac{(b - a)}{4 π K_{0}}$
B

$\frac{(b^{2} - a h)}{4 π K_{0} a b}$
C

$\frac{4 π K_{0}}{(b - a)}$
D

None of these

Solution

$d R_{t} = \frac{d r}{k . A} = \frac{d r}{\frac{k_{0}}{r^{2}} . 4 π r^{2}} = \frac{d r}{4 π k_{0}}$
$∴ R_{t} = \int_{a}^{b} \frac{d r}{4 π k_{0}} = \frac{(b - a)}{4 π k_{0}} .$

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