Examples of thermal radiation in the following topics:
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- Let's imagine a blackbody enclosure, and we stick some material inside the enclosure and wait until it reaches equilibrium with the radiation field, $I_\nu = B_\nu(T)$.
- $\displaystyle \text{Another Kirchoff's Law: }S_\nu = B_\nu(T) \text{ for a thermal emitter}$
- Because $I_\nu=B_\nu(T)$ outside of the thermal emitting material and $S_\nu=B_\nu(T)$ within the material, we find that $I_\nu=B_\nu(T)$ through out the enclosure.
- If we remove the thermal emitter from the blackbody enclosure we can see the difference between thermal radiation and blackbody radiation.
- A thermal emitter has $S_\nu = B_\nu(T)$,$B_\nu(T)$ so the radiation field approaches $B_\nu(T)$ (blackbody radiation) only at large optical depth.
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- We are going to set the stage for a deeper look at astrophysical sources of radiation by defining the important concepts of radiative transfer, thermal radiation and radiative diffusion.
- One can make a large amount of progress by realizing that the distances that radiation typically travels between emission and detection or scattering etc. are much longer than the wavelength of the radiation.
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- This range of wavelengths corresponds to a frequency range of approximately 300 GHz to 400 THz, and includes most of the thermal radiation emitted by objects near room temperature.
- Unlike heat transmitted by thermal conduction or thermal convection, radiation can propagate through a vacuum.
- Humans, their surroundings, and the Earth itself emit most of their thermal radiation at wavelengths near 10 microns, the boundary between mid and far infrared according to the delineation above.
- The range of wavelengths most relevant to thermally emitting objects on earth is often called the thermal infrared.
- Many astronomical objects emit detectable amounts of IR radiation at non-thermal wavelengths.
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- However, it is often convenient to characterize the radiation from astrophysical sources by assuming that it is a blackbody and using some property of the blackbody spectrum to derive a characteristic temperature for the radiation.
- Second if a material is emitting thermal radiation one can obtain a simple expression of the radiative transfer equation (see the problems).
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- Blackbody radiation is a radiation field that is in thermal equilibrium with itself.
- In general we will find it convenient to think about radiation that is in equilibrium with some material or its enclosure.
- Using detailed balance between two enclosures in equilibrium with each other and the enclosed radiation we can quickly derive several important properties of blackbody radiation.
- The intensity ($I_\nu$) of blackbody radiation does not depend on the shape, size or contents of the enclosure.
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- ., if the radiating particles do not have a Maxwellian distribution) one has to use the full expression for the source function; a power-law distribution often occurs astrophysically.
- An extreme example of non-thermal emission is the maser.For atoms in thermodynamic equilibrium we have
- This yields a negative absorption coefficient, so the optical depth decreases and becomes negative as one passes through a region with inverted populations and the intensity of the radiation actually increases exponentially as the magnitude of the optical depth increases.
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- A black body emits radiation called black body radiation.
- Planck described the radiation by assuming that radiation was emitted in quanta.
- A black body in thermal equilibrium (i.e. at a constant temperature) emits electromagnetic radiation called black body radiation.
- Max Planck, in 1901, accurately described the radiation by assuming that electromagnetic radiation was emitted in discrete packets (or quanta).
- Contrary to the common belief that electromagnetic radiation can take continuous values of energy, Planck introduced a radical concept that electromagnetic radiation was emitted in discrete packets (or quanta) of energy.
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- The Zeroth Law of Thermodynamics states that systems in thermal equilibrium are at the same temperature.
- Even if two objects don't touch, heat may still flow between them, such as by radiation (as from a heat lamp).
- If A and C are in thermal equilibrium, and A and B are in thermal equilibrium, then B and C are in thermal equilibrium.
- Temperature is the quantity that is always the same for all systems in thermal equilibrium with one another.
- The double arrow represents thermal equilibrium between systems.
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- In these examples, heat is transferred by radiation.
- There is a clever relation between the temperature of an ideal radiator and the wavelength at which it emits the most radiation.
- The rate of heat transfer by emitted radiation is determined by the Stefan-Boltzmann law of radiation:
- A black object is a good absorber and a good radiator, while a white (or silver) object is a poor absorber and a poor radiator.
- The visible light, although dramatic, transfers relatively little thermal energy.
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- The most important case astrophysically is thermal bremsstrahlung where the electrons have a thermal distribution so the probablility of a particle having a particular velocity is
- We know that radiation comes in bunches of energy $\hbar \omega$ so for a particular frequency $mv^2/2 > h\nu$ for the electron to have enough energy to emit a photon.
- ${\bar g}_{ff}$ is the thermally averaged Gaunt factor.
- Thermal bremsstrahlung spectra for two temperatures that differ by a factor of ten