Question

A very small hole in an electrical furnace used for treating metal acts nearly as black body. If the hole has an area $100m{m}^2$ and it is desired to maintain the metal at ${727}^{o}C$, then how much power travels through the hole?

• A. Zero
• B. 5.7 W
• C. 57 W
• D. 57 kW

Answer 1

The correct option is B 5.7 W

Stefans Law gives the power:

$P=\sigma Ae{T}^4$

where $\sigma$ is Stefan-Boltzmann constant

$e$ = emissivity = 1 for a black body.

i.e. substituting values, we get:

$P=5.7\times {10}^{-8}\times 100\times {10}^{-6}\times 1\times (1000{)}^4=5.7W$

Hence option B is correct.