100
Y. Fouquart and M. Vesperini
The amount of energy which is scattered in all directions (471" steradians) is [J].
dMv = dEvu~cdl
whereas in the solid angle dw' centered on Sf, it is
dUc dtd = Pv(s,s') d 'dE u'Cdt
v
1/
471"
W
v v
5.2 Emission
5.2.1 Thermodynamic equilibrium
(5.14 )
(5.15)
If we consider neither nuclear nor chemical processes, the internal energy of an atom or a
molecule is made of kinetic energy, electronic, vibrational and rotational energy. When a
photon interacts with matter, two cases are possible:
(1) The interaction takes place with no modification to the internal energy: this is a scattering
process. It is approximately the case when the energy levels of the molecule are quantized and
the energy of the photon is very different. Generally, there are interactions of variable strength
but the process can still be considered as scattering: the absorption of a photon causes a
transition to an upper energy level (excited level), with a short life time and the photon is reemitted at the same frequency (the conversion in kinetic energy is negligible). This scattering
process is called coherent. If the molecule comes back to its initial level through a cascade of
transitions, the scattering is incoherent.
(2) In the case of absorption, there is also a transition to a higher level but the molecule which
has absorbed the photon has a collision with other molecules before re-emitting (i.e. within the
life time of the excited level). This is the case of non-radiative transitions which transform the
energy of the photon into thermal (kinetic) energy.
The absorption process corresponds to the transformation of electromagnetic (radiative) energy
into kinetic (thermal) energy, the emission process is the reverse. Since molecular jiggling is
randomly distributed, absorption and emission processes are isotropic, whereas scattering is
anisotropic.
The thermodynamic equilibrium characterizes the state of matter and radiation inside an isolated volume. In these conditions,
• the state of equilibrium is stationary: by virtue of the second principle of thermodynamics,
there is no thermal change without external interaction (cold source)
• temperature is uniform throughout the volume
• the population of the energy levels is given by the Boltzmann's law
(5.16)
• the absorption coefficient equals the emission coefficient (cv = u~b.)
• for a black body the emittance! is such that Cv = 1 at all wavenumber 1/
• the radiation crossing a surface is isotropic and depends only on temperature, due to the
number of collisions per unit time, through the Planck's function Bv(T).
( 5.17)
!the term "emittance" should be preferred to "emissivity" (IAMAP radiation commission, 1978)
Y. Fouquart and M. Vesperini
The amount of energy which is scattered in all directions (471" steradians) is [J].
dMv = dEvu~cdl
whereas in the solid angle dw' centered on Sf, it is
dUc dtd = Pv(s,s') d 'dE u'Cdt
v
1/
471"
W
v v
5.2 Emission
5.2.1 Thermodynamic equilibrium
(5.14 )
(5.15)
If we consider neither nuclear nor chemical processes, the internal energy of an atom or a
molecule is made of kinetic energy, electronic, vibrational and rotational energy. When a
photon interacts with matter, two cases are possible:
(1) The interaction takes place with no modification to the internal energy: this is a scattering
process. It is approximately the case when the energy levels of the molecule are quantized and
the energy of the photon is very different. Generally, there are interactions of variable strength
but the process can still be considered as scattering: the absorption of a photon causes a
transition to an upper energy level (excited level), with a short life time and the photon is reemitted at the same frequency (the conversion in kinetic energy is negligible). This scattering
process is called coherent. If the molecule comes back to its initial level through a cascade of
transitions, the scattering is incoherent.
(2) In the case of absorption, there is also a transition to a higher level but the molecule which
has absorbed the photon has a collision with other molecules before re-emitting (i.e. within the
life time of the excited level). This is the case of non-radiative transitions which transform the
energy of the photon into thermal (kinetic) energy.
The absorption process corresponds to the transformation of electromagnetic (radiative) energy
into kinetic (thermal) energy, the emission process is the reverse. Since molecular jiggling is
randomly distributed, absorption and emission processes are isotropic, whereas scattering is
anisotropic.
The thermodynamic equilibrium characterizes the state of matter and radiation inside an isolated volume. In these conditions,
• the state of equilibrium is stationary: by virtue of the second principle of thermodynamics,
there is no thermal change without external interaction (cold source)
• temperature is uniform throughout the volume
• the population of the energy levels is given by the Boltzmann's law
(5.16)
• the absorption coefficient equals the emission coefficient (cv = u~b.)
• for a black body the emittance! is such that Cv = 1 at all wavenumber 1/
• the radiation crossing a surface is isotropic and depends only on temperature, due to the
number of collisions per unit time, through the Planck's function Bv(T).
( 5.17)
!the term "emittance" should be preferred to "emissivity" (IAMAP radiation commission, 1978)