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The total energy radiated from a black body source is collected for one minute and is used to heat a quantity of water. The temperature of water is found to increase form ${20^o}C$ to ${20.5^o}C$. If the absolute temperature of the black body is doubled and the experiment is repeated with the same quantity of water at ${20^o}C$, the temperature of water will be....... $^oC$
$21$
$22$
$24$
$28$
Solution
(d) The total energy radiated from a black body per minute.
$Q \propto {T^4}$
==> $\frac{{{Q_2}}}{{{Q_1}}} = {\left( {\frac{{2T}}{T}} \right)^4} = 16$
==> ${Q_2} = 16{Q_1}$
If m be mass of water taken and S be its specific heat capacity, then ${Q_1} = ms(20.5 – 20)$ and ${Q_2} = ms(\theta – 20)$
$\theta ^\circ C = $Final temperature of water
==> $\frac{{{Q_2}}}{{{Q_1}}} = \frac{{\theta – 20}}{{0.5}}$
==> $\frac{{16}}{1} = \frac{{\theta – 20}}{{0.5}}$
==> $\theta = 28^\circ C$
