Thermal or Black-Body Radiation |
In General > s.a. radiation [including pressure];
physical constants [Stefan-Boltzmann constant].
* Idea: Radiation emitted by a
perfectly absorbing and emitting body at a fixed temperature T; It
describes (maximum) heat transfer from an object in the far field; The calculation
of its spectrum was "a loose thread that when tugged (by Planck) would
eventually unravel the entire fabric of what had passed for reality."
* Spectrum: It is given by the
Planck distribution
E(f, T) df = (2πh/c2) (f 3 / ehf/kT −1) df .
* Stefan-Boltzmann law: For a
macroscopic black body at temperature T, the total energy emitted per unit
surface and unit time is E = σT 4,
with σ the Stefan-Boltzmann constant.
* Wien's law: For a macroscopic black
body at temperature T, λmax
= (0.0029 m/K) T −1.
* Deviations from the general relations:
When the size of the radiating body approaches the typical wavelength of the emitted
radiation, the spectrum and radiation rate need to be calculated using a more general
and detailed theory rather than following Planck's law, based on fluctuational
electrodynamics and the fluctuation-dissipation theorem, and using the object's
shape and absorption characteristics.
> Online resources:
see Wikipedia's Planck law page.
Phenomenology and Related Effects
> s.a. temperature [and Lorentz transformations].
* Energy-level shifts and induced forces:
Blackbody radiation around hot objects induces ac Stark shifts of the energy levels of nearby
atoms and molecules; These shifts are roughly proportional to the fourth power of the temperature
and induce a force decaying with the third power of the distance from the object.
@ General references: Silva e Costa PLA(04) [as seen by moving observer];
Balasanyan & Mkrtchian a0907 [drag on a relativistic moving mirror];
Sonnleitner et al PRL(13)
+ news pw(13)jul [net attractive force between tiny objects].
@ Radiative heat transfer:
Francoeur & Mengüç JQSRT(08) [and fluctuational electrodynamics];
Golyk et al EPL(13)-a1210 [between curved objects, small-distance expansion];
> s.a. Heat Flow.
References
> s.a. light and thermodynamic systems [thermal light].
@ General: Planck 06;
Agnese et al NCB(99) [simple];
Chang & Guan qp/04 [in a compact space];
Boyer FP(07) [and relativity and discrete charge];
Kramm & Herbert a0801 [using dimensional analysis];
Kramm & Mölders a0901;
Smerlak EJP(11) [more consistent derivation];
Marr & Wilkin AJP(12)may [Planck's law in introductory physics];
Ford & O'Connell PRE(13)-a1310 [Lorentz transformation of blackbody radiation].
@ Quantum aspects:
Boya et al qp/00 [multiphoton states];
Greffet et al Nat(02)mar,
Greffet & Henkel CP(07) [coherent emission];
Johansen JOB(04)qp.
@ History: Wedgwood PTRS(1782);
Boya RACZ(03)phy/04 [Planck 1900];
Varró FNL(06)qp [Einstein's fluctuation formula];
Carvalho Martins a1308-ln [and quantum theory];
Persson AJP(18)dec
[presentation of the history of Planck's blackbody radiation equation];
Boyer AJP(18)jul [in classical electrodynamics].
@ Coupling to atoms: Fröhlich & Merkli CMP(04)mp [return to equilibrium].
@ Classical derivation: Marshall NC(65);
Boyer PRD(84) [from equivalence principle and zero-point radiation].
@ Relativistic: Lee & Cleaver a1507 [inertial and non-inertial reference frames].
@ Quantum-gravity motivated corrections:
Kim et al PRD(07)-a0705 [in κ-Minkowski spacetime];
Mania & Maziashvili PLB(11)-a0911 [minimum-length corrections];
Husain et al PRD(13)-a1305 [and evidence for dimensional reduction];
Ramos & Boschi PhyA(14)-a1404 [with compact extra dimensions].
@ Nanoscale objects: Wuttke & Rauschenbeutel PRL(13)-a1209
+ news pw(12)sep [and fluctuational electrodynamics];
> s.a. QED phenomenology.
@ Other variations: García-García PRA(08)-a0709 [finite-size corrections];
Moreira & Ribeiro a1512
[massive-photon generalization of the Stefan-Boltzmann law];
> s.a. GUP phenomenology.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 20 sep 2020