Substantial Balance Equation of Internal Energy as Viewed by the Balance Theory

The article defines the microscopic substantial system and elementary first-order increments of elementary third-order increments of internal energy (IE), friction heat and heat exchanged between the substantial microsystem and the exterior. A substantial balance of internal energy (IE) has been presented for extensive quantities (EQ) with reference to a substantial microsystem which has been next transformed into a substantial balance equation of the mass density of internal energy (IE). The substantial balance equation of the mass density of internal energy has been integrated for a substantial system throughout the whole substantial area, obtaining a substantial balance equation of internal energy for intensive quantities related to this area. It has also been defined under what conditions this balance equation can be used in the substantial area. In the case of the reversible change, the substantial balance equation of internal energy (IE) for intensive quantities has been reduced to the equation commonly called the first principle of thermodynamics for intensive quantities.