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A spherical black body with a radius of ...

A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be
(a)225 (b)450
(c) 900 (d)1800

Text Solution

Verified by Experts

The correct Answer is:
A
Power radiated = `e_rsigma T^4A` or Power radiated `prop` (surface area)`(T)^4`. The radius is
halved, hence, surface area will become `1/4` times. Temperature is doubled, therefore, `T^4` becomes
16 times.
New power `= (450)(1/4)(16)= 1800 W.`
`:.` The correct option is (d).
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