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Journal Article

#### On the Integral Law of Thermal Radiation

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RussJMathPhys_460.pdf

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##### Citation

Gusev, Y. V. (2014). On the Integral Law of Thermal Radiation.*
Russian Journal of Mathematical Physics,* *21*(4), 460-471. doi:10.1134/S1061920814040049.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0024-756D-8

##### Abstract

The integral law of thermal radiation by finite-size emitters is studied. Two geometrical
characteristics of a radiating body or a cavity, its volume and its boundary area,
define two terms in its radiance. The term defined by the volume corresponds to the Stefan–
Boltzmann law. The term defined by the boundary area is proportional to the third power of
temperature and inversely proportional to emitter’s effective size, which is defined as the ratio
of its volume to its boundary area. This generalized law is valid for arbitrary temperature
and effective size. It is shown that the cubic temperature contribution is observed in experiments.
This term explains the intrinsic uncertainty of the NPL experiment on radiometric
determination of the Stefan–Boltzmann constant. It is also quantitatively confirmed by data
from the NIST calibration of cryogenic blackbodies. Its relevance to the size of source effect
in optical radiometry is proposed and supported by the experiments on thermal emission
from nano-heaters.