Question

A metal ball of surface area $400 cm ^{2}$ and temperature $627^{\circ} C$ is surrounded by a vessel at $27^{\circ} C$. If the emissivity of the metal is 0.7 , then the rate of loss of heat from the ball is $\left(\sigma=5.67 \times 10^{-8} J / m ^{-2}- s - k ^{4}\right)$

• A. $1100 J / s$
• B. $1579.7 J / s$
• C. $1469.6 J / s$
• D. $1290 J / s$

Answer 1

Answer: (C)

$\frac{ E }{ A \times t }=\sigma\left( T ^{4}- T _{ o }^{4}\right)[ T =627+273=900]$
$\left[ T _{ o }=27+273=300\right]$
$\Rightarrow \frac{ E }{ t }=\sigma A \left( T ^{4}- T _{ o }^{4}\right)$
$P =5.67 \times 10^{-8} \times 400 \times 10^{-4}\left[(900)^{4}-(300)^{4}\right]$
$P =5.67 \times 10^{-8} \times 4 \times 10^{-2}\left[6561 \times 10^{8}-81 \times 10^{8}\right]$
$P =22.68 \times 6480 \times 10^{-2}=1469.6 J / S$