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Standard XII

Physics

Temperature

A spherical s...

Question

A spherical steel ball of $12 m m$ diameter is initially at $1000 K .$ It is slowly cooled in a surrounding of $300 K .$ The heat transfer coefficient between the steel ball and the surroundings is $5 W / m^{2} K .$ The thermal conductivity of steel $20 W / m K .$ The temperature difference between the centre and the surface of the steel ball is

Large because conduction resistance is far higher than the convective resistance

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Large because conduction resistance is far less than the convective resistance

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small because conductive resistance is far higher than the convective resistance

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small because conduction resistance is far less than the convective resistance

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Solution

The correct option is D

small because conduction resistance is far less than the convective resistance
Biot number,

$B i = \frac{Conduction resistance : \frac{l}{k A}}{Convection resistance : \frac{1}{h A}} = \frac{h l}{k}$

where $l = \frac{V}{A} = \frac{π}{6} \frac{d^{3}}{π d^{2}} = \frac{d}{6}$

$∴$ $B i = \frac{h}{k} \frac{d}{6} = \frac{5 \times 0.012}{20 \times 6} = 0.0005$

It means that the conduction resistance is far less than convective resistance

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