I would like to get a few things straightened out concerning internal
energy--like what is it.
Suppose we consider a system to be a block sliding on a stationary
horizontal plate. This statement defines the system and describes the
action from an inertial reference frame that is attached to the plate. In
the discussion that follows any energy losses to the system's environment
are considered negligible.
Below are two alternative descriptions of the system's energics. Does
either of these descriptions use the term internal energy in an orthodox
manner?
1. The system's total energy is the kinetic energy of the block plus the
internal energy of the system (the block's internal energy plus the
plate's internal energy). As friction slows the block its kinetic energy
decreases and the system's internal energy increases, with the sum of
these remaining constant.
2. The system's internal energy excludes the system's translational
kinetic energy which is (1/2) (mass of block + mass of plate) (velocity of
the block-plate's center of mass)^2. The system's total energy is then
this translational kinetic energy plus the system's internal energy. As
friction slows the block, the sum of system's translational kinetic energy
and its internal energy remain constant.
Further thoughts: Consider as a system a billiard ball initially sliding
without rotation on a billiard table. The system, the ball and the table,
now contains rotational as well as translational kinetic energy. Would
this system's internal energy include the rotational kinetic energy?