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

1. 450
2. 1000
3. 1800
4. 225

Correct answer: 1800

Solution

The power radiated by a black body is given by Stefan-Boltzmann law: P = σA(T^4), where A is the surface area (4πr²). Halving the radius reduces the area by a factor of 4, and doubling the temperature increases T^4 by a factor of 16. Thus, the new power is 450 × (1/4) × 16 = 1800 W.

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