18.15: Absorption of Radiation
The rate of heat transfer by emitted radiation is described by the Stefan-Boltzmann law of radiation:
where σ is the Stefan-Boltzmann constant, a combination of fundamental constants of nature; A is the surface area of the object; and T is its temperature in kelvins.
The proportionality to the fourth power of the absolute temperature gives a remarkably strong temperature dependence. It allows the detection of even small temperature variations. Images called thermographs can be used medically to detect regions of abnormally high temperature in the body, which can be indicative of disease. Similar techniques can be used to detect heat leaks in homes, optimize the performance of blast furnaces, improve comfort levels in work environments, and even remotely map the Earth's temperature profile.
The Stefan-Boltzmann equation needs only slight refinement to deal with a simple case of an object's absorption of radiation from its surroundings. Assuming that an object with a temperature T1 is surrounded by an environment with uniform temperature T2, the net rate of heat transfer by radiation is as follows:
where e is the emissivity of the object alone. In other words, it does not matter whether the surroundings are white, gray, or black; the balance of radiation into and out of the object depend on how well it emits and absorbs radiation. When T2 > T1, the quantity Pnet is positive, meaning the net heat transfer is from hot to cold.