ThermodynamicsHard

Question

A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were halved and temperature doubled, the power radiated in watt would be

Options

A.225
B.450
C.900
D.1800

Solution

Power radiated ∝ (surface area) (T )4. The radius is halved, hence, surface area will become 1/4 times. Temperature is doubled, therefore, T4 becomes 16 times.
New power = (16) = 1800 W.

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