Question

A metal ball of surface area $200\, cm ^2$, temperature $527^{\circ} C$ is surrounded by a vessel at $27^{\circ} C$. If the emissivity of metal is $0.4$, then the rate of loss of heat is nearly $\left(\sigma=5.67 \times 10^{-8} W m ^{-2} K ^{-4}\right)$

• A. $108\,W$
• B. $168\,W$
• C. $182 \, W$
• D. $192\,W$

Answer 1

Answer: (C)

Rate of heat loss per unit time per unit area $=e\sigma A\left(T^{4} - T_{0}^{4}\right)$
$=0.4\times 5.67\times \left(10\right)^{- 8}\times 200\times \left(10\right)^{- 4}\times \left[\left(800\right)^{4} - \left(300\right)^{4}\right]$
$=5.67\times 0.4\times 2\times \left(10\right)^{- 8 + 2 - 4}\times \left(10\right)^{8}\left[\left(64\right)^{2} - \left(9\right)^{2}\right]$
$=5.67\times 0.8\times 10^{- 2}\left[55 \times 73\right]$
$=18212.04\times 10^{- 2}$
$=182.12 \, W$