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Thermal Radiation
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The thermal energy of a body is stored in the form of oscillations of atoms in it. By having electric charges atoms the movement of these functions as an antenna emitting energy in the form of electromagnetic waves. In this way the bodies emit heat even if they are not in contact with an external medium.
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$\displaystyle\frac{ dQ }{ dt }= \epsilon \sigma S T ^4$
dQ / dt = e * s * S * T ^4
$ q = \epsilon \sigma ( T_c ^4- T_e ^4)$
q = e * s *( T_c ^4- T_e ^4)
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Radiation
Description
Charged particles that oscillate displace their surrounding electric field, generating electromagnetic oscillations. In our world, these oscillations are known as radiation, and depending on their frequency or wavelength, they can manifest as heat, light, or radio waves.
For the particle in question, the emission of radiation corresponds to a loss of energy, and thus, a loss of heat. Similarly, when the particle absorbs radiation from the electromagnetic field in its vicinity, its energy increases, leading to an increase in its temperature.
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Emission of Radiation
Equation
If an object has temperature (energy), its atoms move (displace, oscillate). If this movement involves the displacement of charges, it generates electric fields, which corresponds to the emission of radiation.
The emitted radiation is directly related to the absolute temperature to the fourth power:
| $\displaystyle\frac{ dQ }{ dt }= \epsilon \sigma S T ^4$ |
where:
$S$ is the radiating surface, $\sigma$ is the Stefan-Boltzmann constant ($4.87E-8 kcal/h m^2K^4$ or $5.67E-8 J/s m^2K^4$), $\epsilon$ is the emissivity and $T$ is the absolute temperature.
The emissivity is a factor that depends on the surface's condition, its roughness, and can vary between 0 and 1, typically falling within the range of 0.6 to 0.9.
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Radiative balance
Equation
Not only do we emit radiation, but also the environment around us does so. This means that we also receive radiation, which implies that the external environment also contributes to heating us. Both environments emit radiation according to Stefan-Boltzmann's law:
| $\displaystyle\frac{ dQ }{ dt }= \epsilon \sigma S T ^4$ |
Therefore, the total balance is calculated by subtracting what we receive from what we emit. If the sign is negative, we are losing heat, and if it is positive, we are gaining heat. If the external temperature is $T_e$ and the body's temperature is $T_c$, the balance will be as follows:
Therefore, if the temperatures of the body and the exterior are equal, there is no net radiation, meaning that what we emit is compensated by what we absorb.
| $ q = \epsilon \sigma ( T_c ^4- T_e ^4)$ |
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How a radiator works
Image
Radiators are heated using water that is heated in a central boiler and circulated through the heating system. The heated water warms the metal of the radiators, which, on one hand, heats the surrounding air through convection, creating warmth in the room. They also emit infrared radiation, which can be captured photographically, as illustrated in the following image:
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Video: Thermal radiation