If the temperature of the body is increased by $10\% $ , the percentage increase in the emitted radiation will be ....... $\%$
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(a) $Q \propto {T^4}$ ==> $\frac{{{Q_1}}}{{{Q_2}}} = {\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^4}$
If ${T_1} = T$ then ${T_2} = T + \frac{{10}}{{100}}T = 1.1T$
If ${T_1} = T$ then ${T_2} = T + \frac{{10}}{{100}}T = 1.1T$
==> $\frac{{{Q_1}}}{{{Q_2}}} = {\left( {\frac{T}{{1.1T}}} \right)^4}$ ==> ${Q_2} = 1.46\,{Q_1}$
==> % increase in energy $ = \frac{{{Q_2} - {Q_1}}}{{{Q_1}}} \times 100 = 46\% $
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