First slide

Radiation

Question

When a spherical black body of radius r, having surface temperature $127^{o} C$ is allowed to cool in still air at $27^{o} C$ , its initial rate of cooling is ‘R'. What will be the initial rate of cooling of a black body having surface temperature $227^{o} C$ and radius 2r when allowed to cool in the same environment?

Difficult

A

3.1050 R
B

2.8512 R
C

1.2832 R
D

1.5542 R

Solution

$R = - \frac{d T}{d t} α \frac{1}{γ} (T^{4} - T_{0}^{4})$
$∴ \frac{R^{1}}{R} = \frac{γ}{2 γ} . \frac{{(500)}^{4} - {(300)}^{4}}{{(400)}^{4} - {(300)}^{4}}$
$\Rightarrow R^{1} = \frac{R}{2} (\frac{625 - 81}{256 - 81}) = \frac{R}{2} \frac{544}{175} = 1.5542 R$

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