For a black body at temperature $727^{\circ} C$, its radiating power is $60\; watt$ and temperature of surrounding is $227^{\circ} C$. If temperature of black body is changed to $1227^{\circ} C$ then its radiating power will be ..... $watt$
AIPMT 2002, Medium
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$E \propto (T^{4} - T_0^{4})$
$T_2 = 1227 + 273 = 1500, T_1 = 727 + 273 = 1000 K,$
$T_0 = 227 + 273 = 500 K$
$\frac{{{E_2}}}{{60}} = \frac{{{{(1500)}^4} - {{(500)}^4}}}{{{{(1000)}^4} - {{(500)}^4}}} = \frac{{50625 - 625}}{{10000 - 625}} = \frac{{50000}}{{9375}} \Rightarrow {E_2} = 320\,\,watt$
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