Question

A metal ball of surface area $200c{m}^2$, 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. $108W$
• B. $168W$
• C. $182W$
• D. $192W$

Answer 1

Answer: (C)

Rate of heat loss per unit time per unit area $=e\sigma A\left(T^4-T_0^4\right)$
$=0.4\times 5.67\times {\left(10\right)}^{-8}\times 200\times {\left(10\right)}^{-4}\times \left[{\left(800\right)}^4-{\left(300\right)}^4\right]$
$=5.67\times 0.4\times 2\times {\left(10\right)}^{-8+2-4}\times {\left(10\right)}^8\left[{\left(64\right)}^2-{\left(9\right)}^2\right]$
$=5.67\times 0.8\times 10^{-2}\left[55\times 73\right]$
$=18212.04\times 10^{-2}$
$=182.12W$