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Q.

A composite spherical shell is made up of two materials having thermal conductivities K and 2K respectively as shown in the figure. The temperature at the inner most surface is maintained at T whereas the temperature at the outer most surface is maintained at 10T. The net rate of heat flow from the outermost surface to the innermost surface of shell will be (Neglect any radiation)

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a

$63 π R K T$

b

$72 π R K T$

c

$\frac{432}{7} π R K T$

d

$\frac{147}{2} π R K T$

answer is C.

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Detailed Solution

Thermal resistance $= \frac{R_{2} - R_{1}}{K 4 π R_{1} R_{2}}$
$R_{e q} = \frac{R}{K (4 π) (R) (2 R)} + \frac{R}{(2 K) 4 π (2 R) (3 R)} = \frac{R}{4 π K R^{2}} (\frac{1}{2} + \frac{1}{12}) = \frac{1}{8 π K R} (\frac{7}{6}) = \frac{7}{48 π K R}$

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