First slide

Radiation

Question

A black body at high temperature T K radiates energy at the rate of EW $/ m^{2}$ . When the temperature falls to $(\frac{T}{2}) K,$ the radiated energy will be:

Moderate

A

$\frac{E}{4}$
B

$\frac{E}{2}$
C

2E
D

$\frac{E}{16}$

Solution

$Q \propto T^{4}$
$\Rightarrow \frac{Q_{1}}{Q_{2}} = \frac{{T_{1}}^{4}}{{T_{2}}^{4}} \Rightarrow \frac{E}{E^{'}} = \frac{T^{4}}{{(\frac{T}{2})}^{4}}$
which gives $E^{'} = \frac{E}{16}$

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