First slide

Radiation

Question

Two identical metal balls at temperature $200^{0} C and 400^{0} C kept in air at 27^{0} C . The ratio of net heat loss by these bodies$

Moderate

A

$\frac{1}{4}$
B

$\frac{1}{2}$
C

$\frac{1}{16}$
D

$\frac{473^{4} - 300^{4}}{673^{4} - 300^{4}}$

Solution

If temperature of surrounding is considered, then net loss of energy of a body by radiation
$Q = A \in σ (T^{4} - {T_{0}}^{4}) t \Rightarrow Q directly proportional to (T^{4} - {T_{0}}^{4})$
$\Rightarrow \frac{Q_{1}}{Q_{2}} = \frac{{T_{1}}^{4} - {T_{0}}^{4}}{{T_{2}}^{4} - {T_{0}}^{4}}$
= $\frac{{(273 + 200)}^{4} - {(273 + 27)}^{4}}{{(273 + 400)}^{4} - {(273 + 27)}^{4}}$
= $\frac{{(473)}^{4} - {(300)}^{4}}{{(673)}^{4} - {(300)}^{4}}$

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