Thermal radiation

The third of the thermal processes in essential knowledge 9.3.A.2. Unit 15 supplies the mechanism: 15.4.A.1 states that matter will spontaneously convert some of its internal thermal energy into electromagnetic energy.

Two properties do most of the work in exam scenarios.

• No medium is needed. Radiation crosses a vacuum, so two objects that can see each other are in thermal contact whether or not they touch. The Earth and the Sun are in thermal contact across empty space.
• Every object emits. An object sitting in a room is emitting and absorbing at the same time, and at thermal equilibrium those two rates match.

Where the formula lives matters here. The AP Physics 2 sheet does print $P = A \sigma T^4$, with $\sigma = 5.67 \times 10^{-8}\ \mathrm{W/(m^2 \cdot K^4)}$, but in the Modern Physics group, attached to essential knowledge 15.4.A.3.iii and the blackbody model. No Unit 9 essential knowledge statement uses it. In a Unit 9 question, treat radiation as a pathway to identify; reach for $P = A\sigma T^4$ only when the question is about the power emitted by a blackbody.

The fourth power is why radiation is a footnote for a warm mug and the whole story for a filament. Double the absolute temperature and the emitted power rises by a factor of sixteen.