lobal Journal of Science Frontier Research, A: Physics and Space Science, Volume 24 Issue 4

stopped to this day and from time to time spill out onto the pages of not only scientific forums, but also magazines and books [5...14] contrary to the theorem of E. Noether, which classified them as a consequence of the homogeneity and isotropy of space and time [15]. The fundamental importance of the question of the status of the laws of conservation of energy and quantities of motion of various kinds forces us to look for new ways to resolve this protracted dispute. In this article, the question of the status of conservation principles will be considered from the standpoint of the thermodynamics of irreversible processes [16...18], which made the difference in flows and impulses of energy and its energy carriers especially distinct. II. G eneral C riteria for E nergy C onservation `Differential balance equations for any extensive quantity Θ i (mass M, number of moles of kth substances N k , charge Z, entropy S, etc.), a material carrier of energy (for short, an energy carrier), play a key role in field theory [17]. If the local density ρ i (r,t) = d Θ i /dV of any energy carrier Θ i is arbitrarily distributed in a given volume V, then its change in time d Θ i /dt can be due to two reasons: its transfer across the boundaries of the system d c Θ i /dt =- ∫j i ·df (where j i is the density of its flux through the vector element df of the closed surface of the system in the direction of the external normal n), or the presence inside volume V of sources or sinks of this quantity d i Θ i /dt =∫ σ i dV(where σ i is the density of this source) . If we use the Gauss-Ostrogradsky theorem ∫j i ⋅ df = ∫ ∇⋅ j i dV, this obvious position can be expressed in a simple differential form: d ρ i /dt + ∇⋅ j i = σ i (1) According to (1), any physical quantity Θ i remains unchanged in an isolated system (where ∇⋅ j i = 0) if there is no source in the system ( σ i =0). The question of whether any energy carrier obeys this law can be resolved exclusively experimentally [17]. In particular, the law of conservation of internal energy U, written following N. Umov (1873) in the form [19]: dU/dt +∫j е ⋅ df= 0, (2) (where j е is the energy flux density through the vector element df of the closed surface of a system of constant volume V in the direction of the external normal n), the balance equation without sources corresponds: d ρ е /dt+ ∇⋅ j е = 0. (3) This expression reflects the experimental fact that internal energy U does not simply disappear at some points in space and appear at others but is transferred across the boundaries of the system by an energy flow with density j е , W m -2 (Figure 1). j e n x y z d f r V Fig. 1: The flow of energy across system boundaries To connect the energy flow j е with the energy carrier flows ji, we express it through its components j е i, presenting each of them as a product of the specific energy value (potential) ѱ i = ∂U/∂ Θ i by the energy carrier momentum flux density j i = ρυ i , where ρ = d М /dV is the density of the system, υ i is the transfer speed of the corresponding energy carrier in a fixed coordinate system [18]: j е = Σ i j е i = Σ i ψ i j i , Втм -2 (4) Flows ji also have the meaning of the momentum of thei-th energy carrier, which makes it necessary to distinguish between the concepts of momentum density ρυ (scalar) and its momentum ρ υ (vector). After decomposing ∇ · j е = Σ i ∇ · ( ψ i j i ) into terms Σ i ψ i ∇ j i + Σ i j i · ∇ ψ i , the energy conservation law (3) will take the form [18]: d ρ е /dt =− Σ i ψ i ∇⋅ j i + Σ i x i · j i = 0, (5) where x i ≡ - ∇ ψ i are intensive parameters of the system’s heterogeneity, characterizing the “strength” of the potential field ψ i (thermal, baric, chemical, electrical, etc.) and called “thermodynamic forces in their energy representation” [17]. From this law it directly follows the connection of sources σ i of various energy carriers σ i with energy dynamic forces x i and flows j i : Σ i ψ i σ i = Σ i x i · j i . (6) This relationship is fundamentally different from the dissipative function Тσ s in the thermodynamics of irreversible processes (IP) [16] Т . s = Σ i Х i · J i , (7) (where Х i · J i are thermodynamic forces and flows) in that it does not make entropy a “scapegoat” for any relaxation processes in a nonequilibrium system. It emphasizes that internal sources exist not only for Global Journal of Science Frontier Research ( A ) XXIV Issue IV Version I Year 2024 86 © 2024 Global Journals On the Incompatibility of the Laws of Energy and Pulse Conservation