Calculate the surface temperature of the planet, if the energy radiated by unit area in unit time is $5.67\times10^4\, watt$ : (Planet may be assumed to black body)
Diffcult
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$P=\sigma A T^{4}$
Intensity $\frac{P}{\mathrm{A}}=\sigma \mathrm{T}^{4}$
$\Rightarrow 5.67 \times 10^{4}=5.67 \times 10^{-8} \times \mathrm{T}^{4}$
$\Rightarrow \mathrm{T}^{4}=10^{12}$
$\Rightarrow \mathrm{T}=1000 \mathrm{K}$
$\mathrm{T}=727^{\circ} \mathrm{C}$
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