A set of equations is derived for the conservation of energy of a particle cloud conveyed by gaseous flow, a process common to many energy-conversion schemes. The derivation is developed in logical, sequential steps based on a straight-forward application of fundamental principles. Inclusion of the "boundary" particles in the Eulerian derivations insures the correct limiting single-phase flow equations. The resulting equations form a sound starting point for the development of viable numerical models for many energy-conversion processes.