1.

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

Answer» Correct Answer - 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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