Physics

Problem

For an ideal blackbody, the radiant power emitted per unit surface area depends on the absolute temperature

T

of the body. Which of the following proportionalities is correct? a)

P/A \propto T^{3}

P/A \propto T^{4}

P/A \propto T

P/A \propto T^{2}

Intuitive explanation

The Stefan–Boltzmann law connects thermal radiation to temperature through dimensional analysis and experimental observation. Since power per unit area (intensity) has dimensions of energy/(time·area), and temperature is your only variable, you need to find what power of $T$ makes the dimensions work out. Think about how dramatically objects brighten as they heat up—the relationship is surprisingly steep, not linear.

Intuitive explanation

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