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A black body is at a temperature of 500 K. It emits energy at a rate which is proportional to

Asked in CBSE AIPMT 1997 · Stefan-Boltzmann law

• (1) (500)³
• (2) (500)⁴
• (3) 500
• (4) (500)²

Step-by-step solution

Why the other options are wrong

• (1) comes from a cube is what you would guess if you thought the emission went with the volume of the body; Stefan's law comes from summing the Planck spectrum over all wavelengths and gives a fourth power
• (3) comes from the first power: that is the form of Newton's law of cooling for a small excess over the surroundings, not the emission law of a black body
• (4) comes from a square; no radiation law gives T², and the temperature here is already absolute so there is nothing to convert

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