First slide

Radiation

Question

For most practical temperature we may take it that all bodies radiate heat in proportion to the fourth power of temperature T. If a body (coated black) at 400 K surrounded by atmosphere at 300 Khas cooling rate r₀, the same body at 900 K, surrounded by the same atmosphere, will have cooling rate closer to

Moderate

A

$81 \times 80 r_{0} / 175$
B

$81 r_{0} / 16$
C

$16 r_{0}$
D

$4 r_{0}$

Solution

According to Stefan's law,
$\begin{array}{l} r_{0} = σ (400^{4} - 300^{4}) and r = σ (900^{4} - 300^{4}) \\ \frac{r}{r_{0}} = \frac{\{(900)^{4} - (300)^{4}\}}{\{(400)^{4} - (300)^{4}\}} = \frac{16}{3} \end{array}$
$∴ r = \frac{81 \times 80}{175} r_{0}$

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