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A black body at $227^\circ C$ radiates heat at the rate of 7 cal/$cm^2$ s. At a temperature of $727^\circ C$, the rate of heat radiated in the same units will be
A
80
B
60
C
50
D
112
Detailed Solution
Stefan's law: energy radiated per unit area per second by a black body, $E = \sigma T^4$, so $E \propto T^4$
$T_1 = 227 + 273 = 500$ K; $T_2 = 727 + 273 = 1000$ K
$\frac{E_2}{E_1} = \left(\frac{T_2}{T_1}\right)^4 = \left(\frac{1000}{500}\right)^4 = 2^4 = 16$
$E_2 = 16\times7$
$E_2 = 112$ cal/$cm^2$ s
$T_1 = 227 + 273 = 500$ K; $T_2 = 727 + 273 = 1000$ K
$\frac{E_2}{E_1} = \left(\frac{T_2}{T_1}\right)^4 = \left(\frac{1000}{500}\right)^4 = 2^4 = 16$
$E_2 = 16\times7$
$E_2 = 112$ cal/$cm^2$ s