Question

How to combine the point-particle and real system/extended system analyses of a system to compute changes in the system’s internal energy?

Answer 1

Real system and extended syatem use the actual physical shape of the object,it also contains all forms of energy in the system like Translational, Rotational, Vibrational, Potential, Chemical, It Can have multi-object systems Where as Point particle system is a single point which is located at Center of Mass and Everything else is surroundings.This System only has Translational KE.

In both the cases KINETIC ENERGY is same also  A real system will
have additional behavior due to location of forces. Normal form on a body does work on real syatem but it works on point system.

When we use only point-particle ststem then we must ensure that A point particle can only have translationl KE it has no IE (such as chemical, thermal energy, etc.), no rotational energy, no vibrational energy.

The internal energy of a system can be increased by introduction of matter, by heat or by doing thermodynamic work on the system. When we introduce a point particle system in the real system we consider that our whole mass is concentrated at a point which is given by center of mass which further comes from point particle system but considering the real system along with particle system provides us the validity of internal energy of the system remain conservative only.

Thermodynamic laws explanation about the internal energy exactly matched with the point particle system when we consider its entropy along with the real or extended system type.