Since we feel the heat of the Sun on Earth, even though there is no solid matter between Earth and the Sun to transport it, there must be another mechanism for transferring heat.
As early as 1879, Josef Stefan showed that a black body emits thermal radiation. He found that the radiated power increases proportionally to the fourth power of the temperature. He also found a proportionality between the power and the size of the radiating surface.
The required proportionality constant \(\sigma\) is called the Stefan–Boltzmann constant, since a few years later Ludwig Boltzmann derived this relationship theoretically. It was also found that shiny materials and/or substances that are not completely black emit less power.
The so-called Stefan–Boltzmann law must therefore be multiplied by a temperature-dependent correction factor, the emissivity \(\varepsilon\). The complete formulation is:
$$
P = \varepsilon \sigma A T^4
$$
The Stefan–Boltzmann constant has the value:
$$
\sigma = 5.670374419 \cdot 10^{-8}\,\frac{\mathrm{W}}{\mathrm{m}^2 \cdot \mathrm{K}^4}
$$
This is one of the few laws in which a physical quantity depends so strongly on a parameter.
Humans radiate several kilowatts of power according to this law, but also absorb a large amount of energy from their surroundings, so that an equilibrium is established. In winter, clear starry nights are noticeably colder because clouds absorb radiation from Earth and re-radiate it back to the surface, leading to a higher temperature.
The emissivity of most substances is approximately constant over a wide temperature range. Typical values range from about 0.9 for dark and rough surfaces down to very low values of around 0.01 for highly polished and shiny metal surfaces.
According to Kirchhoff’s law of radiation, good absorbers of radiation are also good emitters, and vice versa. This can be explained qualitatively: all bodies in the universe are constantly absorbing radiation from their surroundings (e.g., from room walls). If absorption were better than emission, heat would flow from colder to warmer bodies, violating the second law of thermodynamics.
In non-contact thermometers (so-called pyrometers), often equipped with a laser pointer for aiming, the thermal radiation of objects is measured. A lens transparent to far infrared is required to focus the radiation. Cost-effective devices typically use polyethylene (PE) lenses. The thermal radiation is then converted into an electrical voltage via heated thermocouples connected in series, which can be immediately converted into a temperature.
A key requirement is knowledge of the emissivity, which can usually be set via a control panel. For medical thermometers (e.g., for measuring fever), the emissivity is often preset for use on the forehead or in the ear.
In addition, thermal imaging cameras can be used to analyze the environment. These usually employ high-quality germanium lenses, which are also transparent to infrared radiation. The sensor consists of a matrix of detectors that, as in pyrometers, convert thermal radiation into electrical signals.
Modern thermal imaging cameras, as demonstrated in experiments, already offer very high resolution, allowing even small structures to be clearly detected.
A thermal image of a human at normal body temperature in front of a wall at room temperature shows the insulating effect of clothing, as the measured temperature is significantly lower in the covered regions.