  Single particle models are sufficient for many topics in introductory physics
courses, but become misleading when applied to situations involving changes in
internal energy. This paper merges two parallel attempts to reform the teaching
of energy in the introductory physics curriculum, resulting in an approach to
internal energy that is conceptually correct, mathematically rigorous, and yet
simple enough for the introductory student to understand. It uses diagrams and
graphs to provide concrete and visual means to track energy storage and
transfer, and takes the smallest possible step in mathematical complexity -
from one-particle to two-particle models - necessary to achieve consistency
with a sound conceptual approach. The mathematical development is guided by the
idea that the term "work" should receive a clear conceptual definition as
energy that is transferred through the boundary of a system; mathematical
expressions are identified as work - of any sort - only when they correspond to
this definition.
