A black body at $227^{\circ} ext{C}$ radiates heat at the rate of $7 ext{ cal cm}^{-2} ext{s}^{-1}$. At a t

Question

A black body at $227^{\circ}	ext{C}$ radiates heat at the rate of $7	ext{ cal cm}^{-2}	ext{s}^{-1}$. At a temperature of $727^{\circ}	ext{C}$, the rate of heat radiated in the same units will be

Accepted Answer

According to Stefan-Boltzmann Law, the energy radiated per unit area per unit time is directly proportional to the fourth power of the absolute temperature of the black body.
$E \propto T^4$
$\frac{E_2}{E_1} = \left(\frac{T_2}{T_1}ight)^4$
Given:
$E_1 = 7	ext{ cal cm}^{-2}	ext{s}^{-1}$
$T_1 = 227^{\circ}	ext{C} = 227 + 273 = 500	ext{ K}$
$T_2 = 727^{\circ}	ext{C} = 727 + 273 = 1000	ext{ K}$
Substituting the values:
$\frac{E_2}{7} = \left(\frac{1000}{500}ight)^4 = 2^4 = 16$
$E_2 = 16 	imes 7 = 112	ext{ cal cm}^{-2}	ext{s}^{-1}$

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