General Thermodynamically Unification of the First and Second Laws of Thermodynamics

The unification of the first and second laws of thermodynamics into a single equation has long been a key goal in thermodynamic research. However, significant mathematical and physical challenges have hindered its achievement. In this paper, we go a step further and seek a general as well as completely thermodynamically unification of these laws. The generality, energy fundamental-based and statistical perspective of the Boltzmann entropy equation can provide a valuable solution to unify the first and second laws of classical thermodynamics. Here, “entropy generation function” is considered as a function that takes a measure of lost available work of any thermodynamic energy conversion system, and also “integrator function” is considered as a function that is applied for the mathematical unification. Also, the quasi-statistical approach of entropy is considered as an approach that studies macroscopic energy components instead of studying the energy of individual particles. So, in this paper, by applying the entropy generation function g, as a novel integrator function, we consider the second law as an equality. In the following, using a new quasi-statistical approach to the entropy with the same base as Boltzmann entropy equation, function g is derived. Finally, we extract two innovative general thermodynamically equations resulting from unification of the first and second laws of classical thermodynamics as well as a novel general thermodynamically unified second law equation is established. Contrary to what is common in classical thermodynamics, the established unified equations are sufficient for the thermodynamically analysis of physical processes, and there is no need to add any additional condition relation or non-thermodynamic quantity. In fact, we are looking for a general thermodynamically unification of the first and second laws, which is one of the highlights of this paper. Finally, a general mathematical-physical validation is presented and in the general case, it is shown that there are no contradictions in the established unified equations.