Ableitung des Stefan'schen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der electromagnetischen Lichttheorie

Boltzmann, Ludwig

doi:10.1002/andp.18842580616

Cited by 274 publications

(145 citation statements)

References 4 publications

Supporting

Mentioning

135

Contrasting

Unclassified

Order By: Relevance

“…Within these limits, it can be shown that the scattering matrix is almost unitary for |m| > ωR while it is approximately zero when |m| < ωR. Therefore, the sum over m at a fixed ω gives a factor of 2ωR proportional to the circumference of the disk in harmony with the blackbody radiation and Stefan-Boltzmann law [43].…”

Section: Thermal Radiationmentioning

confidence: 94%

See 1 more Smart Citation

Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion

2014

View full text Add to dashboard Cite

We study the implications of quantum fluctuations of a dispersive medium, under steady rotation, either in or out of thermal equilibrium with its environment. A rotating object exhibits a quantum instability by dissipating its mechanical motion via spontaneous emission of photons, as well as internal heat generation. Universal relations are derived for the radiated energy and angular momentum as trace formulas involving the object's scattering matrix. We also compute the quantum noise by deriving the full statistics of the radiated photons out of thermal and/or dynamic equilibrium. The (entanglement) entropy generation is quantified and the total entropy is shown to be always increasing. Furthermore, we derive a Fokker-Planck equation governing the stochastic angular motion resulting from the fluctuating backreaction frictional torque. As a result, we find a quantum limit on the uncertainty of the object's angular velocity in steady rotation. Finally, we show in some detail that a rotating object drags nearby objects, making them spin parallel to its axis of rotation. A scalar toy model is introduced to simplify the technicalities and ease the conceptual complexities and then a detailed discussion of quantum electrodynamics is presented.

show abstract

Section: Thermal Radiationmentioning

confidence: 94%

“…Note that the two sets of reference frame are related by Eq. (43) and supplemented by z = z along the symmetry axis of the object. One can then see that the partial wave m is invariant with respect to the reference frame while the frequency is shifted as…”

Section: B Moving Objectsmentioning

confidence: 99%

Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion

2014

View full text Add to dashboard Cite

show abstract

“…As the temperature of a surface increases, so too does the radiance it emits; this is according to the Stefan-Boltzmann Law [16,17]:…”

Section: Thermal Remote Sensing Of Volcanic Activitymentioning

confidence: 99%

Early Analysis of Landsat-8 Thermal Infrared Sensor Imagery of Volcanic Activity

Blackett

2014

Remote Sensing

View full text Add to dashboard Cite

Abstract:The Landsat-8 satellite of the Landsat Data Continuity Mission was launched by the National Aeronautics and Space Administration (NASA) in April 2013. Just weeks after it entered active service, its sensors observed activity at Paluweh Volcano, Indonesia. Given that the image acquired was in the daytime, its shortwave infrared observations were contaminated with reflected solar radiation; however, those of the satellite's Thermal Infrared Sensor (TIRS) show thermal emission from the volcano's summit and flanks. These emissions detected in sensor's band 10 (10.60-11.19 µm) have here been quantified in terms of radiant power, to confirm reports of the actual volcanic processes operating at the time of image acquisition, and to form an initial assessment of the TIRS in its volcanic observation capabilities. Data from band 11 have been neglected as its data have been shown to be unreliable at the time of writing. At the instant of image acquisition, the thermal emission of the volcano was found to be 345 MW. This value is shown to be on the same order of magnitude as similarly timed NASA Earth Observing System (EOS) Moderate Resolution Imaging Spectroradiometer thermal observations. Given its unique characteristics, the TIRS shows much potential for providing useful, detailed and accurate volcanic observations in the future.

show abstract

“…As the temperature of a surface increases, so too does the total radiated energy flux; this is according to the StefanBoltzmann Law (Stefan 1879, Boltzmann 1884):…”

Section: Infrared Remote Sensingmentioning

confidence: 99%

Evaluation of SWIR-based methods for quantifying active volcano radiant emissions using NASA EOS-ASTER data

Wooster

2011

Geomatics, Natural Hazards and Risk

View full text Add to dashboard Cite

Analysis of thermally emissive volcanic features using satellite infrared remote sensing has been conducted over recent decades, primarily using shortwave and thermal infrared (SWIR; TIR) radiance data. The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), mounted on the Earth Observation System (EOS) Terra satellite, offers an advance on earlier instruments, having more bands covering the SWIR atmospheric window and offering a wider dynamic range. This paper compares methods used to analyse ASTER SWIR imagery of active volcanoes, using both simulated cases and actual ASTER imagery of Lascar Volcano, and focuses on radiative power estimates. Those based on the Oppenheimer approach are found to be most reliable for simulated surfaces, with the Lombardo and Buongiorno and Dozier retrievals having larger uncertainties in most cases. However, the Dozier Method results in the highest proportion of successful retrievals, the reliability of which is influenced by factors including band combination, gain setting and saturation. The radiative power metric is shown as a more reliable measure than sub-pixel characterisations of hotspot temperature and area, as retrieved by these methods. We conclude with an assessment of ASTER in terms of its utility for providing quantitative observations of active volcanic surfaces.

show abstract

Ableitung des Stefan'schen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der electromagnetischen Lichttheorie

Cited by 274 publications

References 4 publications

Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion

Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion

Early Analysis of Landsat-8 Thermal Infrared Sensor Imagery of Volcanic Activity

Evaluation of SWIR-based methods for quantifying active volcano radiant emissions using NASA EOS-ASTER data

Contact Info

Product

Resources

About