Question

A very small hole in an electric furnace is used for heating metals. The hole neraly acts as a black body. The area of the hole is $200$ $m{m}^2$ To keep a metal at ${727}^{o}C$, heat energy flowing through this hole $persec$, in $joules$ is:

[$\sigma =5.67\times {10}^{-8}W{m}^{-2}{K}^{-4}$]

• A. $22.68$
• B. $2.268$
• C. $1.134$
• D. $11.34$

Answer 1

Answer: (D)

$11.34$

Given :$A=200m{m}^2=0.0002m^2$ $e=1$ $\sigma =5.67\times {10}^{-8}$ $W{m}^{-2}{K}^{-4}$

Temperature of the metal: $T={723}^{o}C=1000K$

Heat radiated per second: $P=\sigma Ae{T}^4$

$\therefore$ $P=5.67\times {10}^{-8}\times 0.0002\times 1\times (1000{)}^4=11.34J/s$