First slide

Radiation

Question

Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively. The energy radiated per second by the first sphere is

Moderate

A

greater than that by the second
B

less than that by the second
C

equal in both cases
D

the information is incomplete to draw any conclusion

Solution

The energy radiated per second E, by a body of surface area A, at temperature T K is given by
$E = {kσAT}^{4}$ (Stefan's law)
where k = relative emissivity
E₁ = energy radiated per second by
first sphere
$\begin{array}{l} = kσ \{4 π (1)^{2}\} (4000)^{4} \\ = kσπ (1024 \times 10^{12}) joule \end{array}$
Similarly,
$\begin{array}{l} E_{2} = kσ \{4 π (4)^{2}\} (2000)^{4} \\ = kσπ (1024 \times 10^{12}) jojle \end{array}$
$∴ E_{1} = E_{2}$

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