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A block having some emissivity is maintained at 500 K temperature in a surrounding of 300 K temperature. It is observed that, to maintain the temperature of the block, 210 W external power is required to be supplied to it. If instead of this block a black body of same geometry and size is used ,700 W external power is needed for the same. The emissivity of the material of the block is __________.

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answer is 0.3.

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Detailed Solution

If emissivity of body is e, we use
Power required = Radiation rate

$P = σeA (T^{4} - T_{o}^{4})$ ………..(i)

For a block body $P_{B} = σA (T^{4} - T_{o}^{4})$ ………….(ii)

$\frac{(i)}{(ii)} gives \frac{P}{P_{B}} = e \Rightarrow e = \frac{210}{700} = 0 .3$

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