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 $ \left(\sigma=5.67\times10^{-8} Wm^{-2}\, K^{-4}\right) $

• 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
$E \propto T^{4}$
$E=\sigma \cdot A T^{4}$
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} $
$=5.67 \times 2 \times 10^{-12} \times 10^{12}$
$=11.34 \,J / s$