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A small sphere at temperature T radiates onto a black metal foil placed a distance d away, delivering power P to the foil. If both the temperature and the distance are doubled, what power does the foil now receive?

1. 16 P
2. 4 P
3. 2 P
4. P

Correct answer: 4 P

Solution

Power on the foil scales as T⁴/d²; doubling both gives a factor 2⁴/2² = 16/4 = 4, so the foil receives 4P.

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