Question

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

Answer 1

If emissivity of body is $e$, we use
Power required $=$ Radiation rate
$P=\sigma e A\left(T^{4}-T_{5}^{4}\right)$.....(i)
For a block body $P_{B}=\sigma A\left(T^{4}-T_{5}^{4}\right)$ .....(ii)
$\frac{\text { (i) }}{\text { (ii) }} \text { gives } \frac{P}{P_{B}}=e $
$\Rightarrow e=\frac{210}{700}=0.3$