Emission of Heat Radiation

In 1792, Pierre Prevost published what is now called the theory of exchange of heat: every body, at every temperature above absolute zero (0 K), continuously radiates thermal energy, and simultaneously absorbs radiation arriving from its surroundings. The amount of thermal radiation emitted per unit time by a body depends on the nature of its emitting surface, the surface's area, and its temperature -- hotter bodies always radiate at a higher rate than cooler ones, and light-coloured surfaces reflect (rather than absorb) most visible radiation while dark surfaces absorb most of it.

For any body, absorbed radiation adds energy that increases the kinetic energy of its constituent atoms/molecules oscillating about their mean positions -- and since average translational kinetic energy is what determines temperature (Section 3.7), absorbed radiation raises the body's temperature. At the same time, the body's own continuous emission removes energy and tends to lower its temperature. So: if a body radiates more than it absorbs, its temperature falls; if it absorbs more than it radiates, its temperature rises. When the rates of absorption and emission are exactly equal, the temperature stays constant, and the body is said to be in thermal equilibrium with its surroundings -- exactly as with a cup of hot tea or a plate of ice on a table, both of which settle to room temperature over time even though, at room temperature, every object continues both emitting and absorbing radiation simultaneously (just at matched rates).

Colour and temperature. At everyday/room temperatures (more precisely, for temperatures below roughly 800 ºC), the thermal radiation emitted lies at wavelengths longer than visible light, so we cannot see it directly. As a body is heated further, the radiated energy shifts to shorter wavelengths: around 800 ºC, enough of the emission falls in the visible range that the body visibly glows red; by around 3000 ºC (the operating temperature of a tungsten lamp filament, for instance), it glows white-hot. This progression -- invisible, to red-hot, to white-hot -- is a direct, everyday manifestation of the wavelength shift with temperature explored quantitatively in Section 3.14 (Wien's displacement law).

Emissive power. The total heat radiated by a body, $Q$, is found to depend on the body's absolute temperature $T$, the nature of its surface (material, polish, etc.), its surface area $A$, and the time duration $t$ for which it radiates -- and $Q$ is directly proportional to both $A$ and $t$. It is therefore convenient to define the emissive power (or radiant power), $R$, as the heat radiated per unit area per unit time:

$R = \dfrac{Q}{At}$ …