Internal Heat Energy, Entropy and The Second Law: A New Perspective in Theoretical Thermodynamics

In thermodynamics, the internal heat energy that denotes the energy of thermal motion within the system has not been well defined, it is a thermodynamic state function but was lost in current theories. We present a new state function, the internal heat energy of the system into thermodynamics, it implies that the energy classification for the internal energy will be completed. We present a new expression to represent the definition of the entropy according to the state property of the system, which does not need to depend on reversible processes. We find that the entropy production involves three positive definite sources; the driving forces of irreversible processes are derived from the gradients of four thermodynamic forces; and, the second law root in a fundamental principle: the gradients of the four thermodynamic forces spontaneously tend to zero.