- All matter emits/absorbs
electromagnetic radiation (EMR)
from/into its own heat energy pool
by various microscopic processes---which are
transitions
and charge
accelerations
brought about by thermal interactions.
That matter always does this
is due to a
combination of physical laws,
most prominently quantum mechanics
and the
2nd law of thermodynamics.
This kind of EMR is thermal radiation.
- By
"from/into its own heat energy pool",
we mean that the EMR is
NOT reflected EMR.
Reflection is a process in which the EMR does NOT strongly interact with a body or change its state. In reflection, EMR just "bounces off" the body surface changing the surface state only temporarily and briefly in an ideal case.
Of course, bodies usually emit thermal radiation AND reflect EMR at the same time.
- To qualify slight the above statement 1, to emit
thermal radiation
a body must have temperature above
absolute zero
(i.e., 0
kelvins (K)).
However, this case is virtually always the case.
- Dense materials (i.e., solids,
liquids, and
dense gases) have
a continuum
(insofar as we know)
of emission and absorption channels that extend effectively
over all wavelengths
that are practically accessible: i.e., over all the
electromagnetic spectrum
that is practically accessible.
So they radiate
and absorb
continuous spectra.
Recall continuum means there are NO "missing points". The real numbers are a continuum of numbers. Integers and rational numbers are NOT continuums.
Actually crystalline solids like rocks can have broad emission and absorption bands (HI-92), and so do NOT necessarily radiate a continuum. We will NOT go into that detail here.
- Dilute gases
have emission line spectra
in emission and
absorption line spectra
in absorption.
Actually, they always have weak (sometimes very weak)
continuum emission
and absorption too.
We will NOT discuss
line spectrum further here.
- A dense body at a SINGLE
temperature
will emit---NOT counting any
reflection---blackbody radiation
with a blackbody spectrum.
The blackbody spectra for 3 temperatures are illustrated in Image 1.
The blackbody spectra only depend on the temperature of the emitting body, NOT on any other properties: e.g., density (as long as sufficiently high), chemical composition, and shape. This remarkable fact is a result of thermodynamics.
- The formula for
blackbody spectra is
Planck's law
2hc**2 1 B_λ(T) = ------ ---------- , λ**5 [exp(x)-1]where the Planck constant h = 6.62607015*10**(-34) J·s (exactly), the vacuum light speed c = 2.99792458*10**8 m/s (exactly) ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns, and the x = hc/(kTλ), where the Boltzmann contant k = 1.380649*10**(-23) J/K (exactly). For reference for the fundamental physical constants, see also NIST: Fundamental Physical Constants.
Note that Planck's law can be regarded as a function of wavelength λ with temperature T as a parameter or as a function of both wavelength λ and temperature T.
- Blackbody radiation
is the simple limiting case
of thermal radiation.
Actually, many examples of thermal radiation approximate blackbody radiation so closely that they are just considered blackbody radiation. In fact, thermal radiation can often be considered as consisting of a mixture blackbody radiations of different temperatures.
Also actually, thermal radiation and blackbody radiation are often used loosely as synonyms. Thermal radiation that is NOT blackbody radiation just being thought of as non-ideal blackbody radiation.
- Image 2 Caption:
Blackbody spectra
for temperatures between
100 K and 10**4 K plotted on a
log-log plot.
The blackbody spectrum for T = 5777 K approximates the solar spectrum as seen above the Earth's atmosphere. The solar photosphere effective temperature = 5777 K. Effective temperature of a body (e.g., star or planet) is the temperature a perfect blackbody radiator (with a radius equal to the defined radius of the body) that radiates exactly as much radiant flux as the body.
Effective temperatures for stars are usually good average temperatures for their stellar photospheres.
The blackbody spectrum for T = 300 K approximates those for the Earth and the human body.
- Note that the maximum
of the blackbody spectrum
on the
log-log plot in Image 2 shifts
with wavelength
with temperature
in a systematic way.
The wavelength of
the maximum,
in fact, obeys
Wien's law
which is explicated in detail file
wien_law.html
(see also
Wikipedia:
Wien's displacement law: Derivation from Planck's law).
However, to give the short explication,
for a blackbody spectrum,
Wien's law states
that the maximizing wavelength
λ_max = hc/(x_max*kT) = (2897.771955185172661 ... μm-K)/T,
and so is
inversely proportional
to temperature T: i.e.,
λ_max ∝ 1/T.
Thus, temperature as
a function of
maximizing wavelength obeys
the inverse Wien's law
T = hc/(x_max*λ_max*k)=(2897.771955185172661 ... μm-K)/λ_max.
Therefore if we constrain
Planck's law by
inverse Wien's law,
we get a curve which is the
maximum of blackbody spectrum
as just a function
of maximizing wavelength: i.e.,
2hc**2 1 B_λ[T(λ)]max = ------ -------------- ∝ λ**(-5) , λ**5 [exp(x_max)-1]where one constrains x = x_max = hc/(kTλ) = (4.965114231744276303 ...) which is just a constant. Note that B_λ[T(λ)]max is power law with power p = -5, and so should be a straight line on the log-log plot in Image 2 with slope = -5---which is, in fact, the case. A rough calculation from the log-log plot values gives
slope = (-1-9)/(1.5-0.5) = -5
using the fact that log(0.3) ≅ -1/2 and log(30) ≅ 3/2. We get the exact result -5 fortuitously. - In fact, the name
blackbody radiation
is NOT very good since the a body emitting it
is often NOT black.
In fact, to the human eye,
it can have a colors
and look very bright
depending on temperature as we
discuss below
and how much EMR
it reflects.
If the temperature of the emitting body is very low and there is NO reflection, then yes a blackbody radiator will look black to the human eye
In any case, tradition (beginning in the 19th century) has stuck us with the name blackbody radiation. Thermodynamic equilibrium thermal radiation would be a more accurately descriptive, if longwinded, name.
- Blackbody radiation
itself (NOT just its
emitting body the blackbody radiators)
has the temperature
that appears in
Planck's law.
Usually, this will be the
temperature of the
emitting body.
However,
adiabatic expansion/contraction
of the space occupied by
the blackbody radiation
can cause the
blackbody radiation
temperature to change independent
of matter.
A very important special case of change is that
cosmic background radiation (CBR)
cools with the
expansion of the universe
and now is the
cosmic microwave background (CMB)
with CMB temperature = 2.72548(57) K (Fixsen 2009).
- If blackbody radiation
and the matter it is in contact with
have the same temperature, then
the two are in
thermodynamic equilibrium
with respect to each other.
- UNDER RECONSTRUCTION BELOW
- A perfect blackbody spectrum
is a smooth spectrum that reaches from zero to infinite
wavelength.
A perfect blackbody spectrum is an ideal limiting case, but very nearly perfect ones occur both in nature and in the laboratory and many objects (e.g., stars) approximate blackbody radiators to one degree or another.
- The temperature of
blackbody radiation is always specified
on the Kelvin scale.
The zero point of the Kelvin scale (i.e., T = 0 K) is absolute zero---which is the coldest possible state where all heat energy that can be removed has been removed.
If true a blackbody radiator was at absolute zero (where there is no heat energy to radiate) and was NOT reflective, it would be black.
- The classical Rayleigh-Jeans law
for T = 5000 K is also shown in the image.
Rayleigh-Jeans law asymptotically agrees with the correct blackbody spectrum in the limit that wavelength λ goes to infinity. But as λ goes to zero, the Rayleigh-Jeans law predicts infinite energy. This is the famous ultraviolet catastrophe which, when it was first noticed, was a clue that classical physics failed outside of what we now call the classical realm.
- Note the plot illustrates that
as temperature
increases/decreases the spectra become bluer/redder (more dominated by blue/red light).
- What color does the
human eye
with its peculiar
psychophysical response
see for a blackbody spectrum?
For both photopic vision (i.e., human eye psychophysical response under well lit conditions) and scotopic vision (i.e., human eye psychophysical response under dimly lit conditions), it seems that ∼ 1500--11000 K is white hot (see Temperature of a "White Hot" Object, Carine Fang, 2001, bottom of page); going lower in temperature would lead orange to red hot to just visible red hot at ∼ 750 K; going higher temperature would lead to blue hot (see Wikipedia: Thermal radiation: Subjective color to the eye of a black body thermal radiator; Wikipedia: Red heat).
However, for viewing stars at night, the colors are modified by the Earth's atmosphere which preferential scatters blue light which is why day sky is blue (see Wikipedia: Diffuse sky radiation).
For example, reddish stars seen in visual astronomy have photospheric temperature which would make them look white hot if seen by visual astronomy in space. it seems that apparent colors are a bit different: star orange-red: ∼ ≤ 3700 K, star yellow-orange: ∼ 3700--5200 K, star yellow-white: ∼ 5200--6000 K (e.g., the Sun), star white: ∼ 6000--7500 K, star white to blue-white: ∼ 7500--10,000 K, star blue-white: ∼ 10,000--30,000 K, star blue: ∼ ≥ 30,000 K (Star Colors Explained, Brian Ventrudo, 2008 December 23).
Blue hot is seldom seen in everyday life, but hot young OB stars (T ∼ ≥ 30,000 K: Wikipedia: O-type main-sequence star: Properties) are star blue---though no star in the sky as ever looked blue to yours truly. OB stars give the blue color (∼ 0.450--0.495 μm) to the spiral arms of spiral galaxies that you often see in images of spiral galaxies. I think this blue color (∼ 0.450--0.495 μm) in the images is meant to be true color---no one ever says it isn't.
- Is there a green hot?
NO. Even when a blackbody spectrum
peaks in the
green color band (∼ 0.495--0.570 μm),
the mixture of
colors never looks
green
to the human eye.
See blackbody keywords below (local link / general link: blackbody_keywords.html).
See the
Blackbody radiation videos
below
(local link /
general link: blackbody_videos.html).
EOF
