Stefan-Boltzmann law

Required content in AP Physics 2, not an extra. Essential knowledge 15.4.A.3.iii states that the rate at which energy is emitted (power) by a blackbody is proportional to the surface area of the body and to the temperature of the body raised to the fourth power, and it names the Stefan-Boltzmann law.

Printed in the Modern Physics group of the AP Physics 2 sheet, with $\sigma = 5.67 \times 10^{-8}\ \mathrm{W/(m^2 \cdot K^4)}$ in the constants table.

What each symbol carries. $P$ is radiated power in watts, $A$ the emitting surface area in square metres, $T$ the absolute temperature in kelvin. Convert a Celsius reading first: the law is written for absolute temperature, and a ratio of Celsius readings is not a ratio of temperatures.

The fourth power is where the marks are. Suggested skill 2.C for Topic 15.4 is comparing a quantity between two scenarios, and this equation rewards a ratio more than a calculation. Double $T$ and the emitted power rises by $2^4 = 16$. Triple it and the rise is $3^4 = 81$. Area scales only linearly, so a small hot filament outradiates a large warm wall.

Where the law lives. It sits in Unit 15 with the blackbody model, not in the Unit 9 heat transfer topic where thermal radiation is first named. Reach for it when a question asks for emitted power, not when it asks you to name a transfer pathway. Wien's law locates the peak of the same spectrum; this one totals it.