  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.
