The methods of energy transfer and transformation in macroscopic systems are of importance in various areas of science and technology, such as power and heat engineering, chemistry, aerospace technologies, mechanical and biomedical engineering, etc. That is why the present work is topical. Its main target is application of the molecular-kinetic concepts at introducing the equation of the first law of thermodynamics. When presenting this law in textbooks, some troubles appear in differentiating between energy (energy change) and heat or work as well as between heat and work. Therefore the present paper contains a critical analysis of the methods of introducing miscellaneous equations of energy for a closed system and flux, as well as the concepts of heat, work and energy in the scientific literature. By using mathematical manipulations of the Newton's second law written for each single microparticle, a transition is made to the law of energy change (known as the first law of thermodynamics) of all microparticles of a system. Based on the molecular-kinetic concepts, rigorous definitions of such physical quantities as heat and work are formulated.