Mathematical Analysis for Radiometric Calorimetry of a Radiating Sphere

Equations are derived from which the temperature dependence of both the specific heat and the thermal diffnsivity of a spherical sample of material can be calculated from observations of the time dependence of the surface temperature and the time-rate of energy loss from the sample as it cools. The derivation takes into account the non uniformity of the interior temperature field of the sample, and the resulting equations can be applied not only to radiative cooling, but also to any other cooling mechanism that does not violate the assumed spherical symmetry. The analysis excludes change of phase, but it does take thermal expansion into account. To permit the making of estimates neeessary for the design of radiative cooling experiments, a universal temperature-time cooling curve is derived for the post-transient cooling regime of a radiating sphere of any size with arbitrary, but constant, thermal parameters.