Skip to main content
SpringerLink
Log in

Deviations from the Stefan Boltzmann law at low temperatures

  • Contributed Papers
  • Published:
Applied physics Aims and scope Submit manuscript

Abstract

The total radiation energy in a cavity is studied in the limit of small volume and temperature. The validity of refined high-temperature expansions is examined. For the cube-shaped cavity with edge lengthL complete results covering the range 0≦LT<∞ are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

k :

Boltzmann constant

T :

absolute temperature

h :

Planck's constant

h :

Dirac's symbolh/2π

c :

velocity of light

V :

volume of cavity

K :

degree Kelvin

cm:

centimeter

v i :

frequency of thei-th cavity mode

g i :

weight ofv i

\(\bar D(v)\) :

averaged mode density of cavity radiation

L :

edge length of cube shaped cavity, length of cylinder shaped cavity

ϑ:

order of

γ:

circumference of cylindrical cavity

γ i :

i-th smooth piece of γ

α j :

j-th corner angle of γ

A :

effective length in second order correction of mode density

K :

curvature of γ i

R :

radius of cylinder shaped cavity

E :

exact total radiation energy

E i :

i-th term in the high-temperature expansion ofE

E *i :

i-th term in the low-temperature expansion ofE

p :

diameter-to-length ratio=2R/L for cylindrical cavities

j s, l :

s-th zero of Bessel functionJ l(x)

j's, l :

s-th zero of derivative of Bessel function,J'l(x)

References

  1. L.Boltzmann: Ann. Phys.258, 291 (1884)

    Google Scholar 

  2. W.R.Blevin, W.J.Brown: Metrologia7, 15 (1971)

    Article  ADS  Google Scholar 

  3. D.Bijl: Phil. Mag.43, 1342 (1952)

    Google Scholar 

  4. H.P.Baltes: Helv. Phys. Acta44, 589 (1971)

    MathSciNet  Google Scholar 

  5. K.M.Case, S.C.Chiu: Phys. Rev.A1, 1170 (1970)

    Article  ADS  Google Scholar 

  6. H.P.Baltes: Phys. Rev.A6 (1972)

  7. H.P.Baltes, F.K.Kneubühl: Helv. Phys. Acta45, 481 (1972). (Dissertation No. 4776, ETH Zürich 1971)

    MathSciNet  Google Scholar 

  8. R.Balian, C.Bloch: Ann. Phys.64, 271 (1971)

    Article  ADS  MathSciNet  Google Scholar 

  9. H.P.Baltes, F.K.Kneubühl: Opt. Comms.4, 9 (1971)

    Article  ADS  Google Scholar 

  10. C.Schaefer: Z. Phys.7, 287 (1921)

    Article  ADS  Google Scholar 

  11. K.Pöschl:Mathematische Methoden der Hochfrequenztechnik (Springer-Verlag, Berlin-Göttingen-Heidelberg 1956)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Freie Universität Berlin, F. B. 20, D-1000, Berlin 33, Germany

    H. P. Baltes

Authors
  1. H. P. Baltes
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baltes, H.P. Deviations from the Stefan Boltzmann law at low temperatures. Appl. Phys. 1, 39–43 (1973). https://doi.org/10.1007/BF00886803

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00886803

Index Headings

Search

Navigation