A metallic sphere having inner and outer radii ‘a’ and ‘b’ respectively has thermal conductivity K=K0/r2a ≤ r≤bwhere K0 is a constant. The thermal resistance between inner and outer surface is

dRt = drk.A=drk0r2 . 4πr2=dr4πk0∴ Rt= ∫abdr4πk0= b−a4πk0.

A metallic sphere having inner and outer radii ‘a’ and ‘b’ respectively has thermal conductivity K=K0/r2a ≤ r≤bwhere K0 is a constant. The thermal resistance between inner and outer surface is

dRt = drk.A=drk0r2 . 4πr2=dr4πk0∴ Rt= ∫abdr4πk0= b−a4πk0.

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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

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$\frac{(b - a)}{4 π K_{0}}$

$\frac{(b^{2} - a h)}{4 π K_{0} a b}$

$\frac{4 π K_{0}}{(b - a)}$

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answer is A.

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$d R_{t} = \frac{d r}{k . A} = \frac{d r}{\frac{k_{0}}{r^{2}} . 4 π r^{2}} = \frac{d r}{4 π k_{0}}$

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

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A metallic sphere having inner and outer radii ‘a’ and ‘b’ respectively has thermal conductivity K=K0/r2a ≤ r≤bwhere K0 is a constant. The thermal resistance between inner and outer surface is

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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