According to the Stefan-Boltzmann law, the power radiated by a black body is proportional to:

Solution

Physics sir · 3 steps

Radiated power climbs with the fourth power of absolute temperature, so a little heating goes a long way.

1. The law. A black body of surface area A at absolute temperature T radiates energy per second given by the Stefan-Boltzmann law.

   P = σ A T⁴

2. Read the dependence. Here σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ is a constant and A is fixed for a given body. The only variable left is T, and it appears to the fourth power, so doubling T makes P grow 2⁴ = 16 times.
3. So. The power radiated by a black body is proportional to T⁴, which is option (d).

The idea to keep. Stefan-Boltzmann: P = σ A T⁴, with T always in kelvin. For a body losing heat to surroundings at T₀, the net power goes as T⁴ - T₀⁴.

Answer from the NTA final answer key. Solution by PrepWiser.