Question

A very small hole in an electric furnace is used for heating metals. The hole nearly acts as a black body. The area of the hole is $200 \, mm^{2}$ . To keep a metal at $727 \,{}^\circ C$ , heat energy flowing through this hole per sec, in joules, is ( take $\sigma =5.67\times 10^{- 8} \, W \, m^{- 2} \, K^{- 4}$ )

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

Answer 1

Answer: (D)

By Stefan's law,
if the absolute temperature of a black body is $T$ , then the energy $E$ emitted per second per unit surface area of the body
$E \propto T^{4}$
$E \, =\sigma \, AT^{4}$
Given,
$\sigma =5.67\times 10^{- 8} \, W \, m^{- 2} \, K^{- 4}$
$T=727+273=1000 \, K$
$A=200\times 10^{- 6} \, m$
$E=5.67 \times 10^{-8} \times\left(200 \times 10^{-6}\right) \times(1000)^4$
$=5.67\times 2\times 10^{- 12}\times 10^{12}$
$=11.34 \, J \, s^{- 1}$