On the integral law of thermal radiation

TL;DR

This paper investigates how the size and shape of thermal emitters influence their radiance, revealing a boundary-area term that affects measurements and is supported by experimental data from cryogenic blackbodies and nano-heaters.

Contribution

It introduces a generalized integral law of thermal radiation incorporating boundary effects, supported by experimental validation across different temperature regimes.

Findings

Boundary-area term affects radiance measurements.

Cubic temperature contribution observed in experiments.

Size of source influences optical radiometry accuracy.

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 the emitter's effective size, which is defined as the ratio of its volume to its boundary area. 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. The conjecture that this generalized law is valid for arbitrary temperature and effective size is supported by the experiments on thermal emission from nano-heaters.