thermal radiation

Examples of thermal radiation in the following topics:

• Thermal Radiation

  • 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.

• Introduction

  • 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.

• Infrared Waves

  • 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.

• Blackbody Radiation

  • 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).

• A Physical Aside: Intensity and Flux

  • 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.

• Non-Thermal Emission

  • ., 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.

• Planck's Quantum Hypothesis and Black Body Radiation

  • 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.

• The Zeroth Law of Thermodynamics

  • 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.

• Radiation

  • 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.

• Thermal Bremsstrahlung Emission

  • 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