Q.

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

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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

answer is C.

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Detailed Solution

The energy radiated per second E, by a body of surface area A, at temperature TK is given byE=kσAT4 [Stefan's law)where k = relative emissivityE1 = energy radiated per second by first sphere =kσ4π(1)2(4000)4                  =kσπ1024×1012 joule Similarly, E2=kσ4π(4)2(2000)4                   =kσπ1024×1012 joule ∴ E1=E2
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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