Global Journal of Science Frontier Research, A: Physics and Space Science, Volume 23 Issue 1

forming a vector with other quantities. For example, in [10] V. Hamity represents this thermodynamical parameter as T v ˆ µ µ =Θ , ,3,2,1,0 = µ (15) where µ v is a unit 4-vector in Minkowski space, moreover = µ v [ α vv , 0 ], α =1,2,3, (16) i.e., ≡ α v v is a velocity vector in Euclidean space; 1 = µ µ vv . (17) Further, developing the idea of temperature vector representation, the author of [10] finally comes to the following expression: kT v / µ µ β = , (18) with ( ) 0,0,0, β β µ = , then kT / 0 µ µ δ β = ,             = 1000 0100 0010 0001 ν µ δ . (19) Other authors, e.g., [12], also tried to represent the relativistic temperature exclusively as a vector. However, in our opinion, this approach to the problem is incorrect, since the photon gas in the cavity is a continuous medium. Then an expanded tensor approach is necessary to describe energy processes in it. In this case the second thermodynamics law can be represented in Minkowski space as ,4,3,2,1 , ;4,3,2,1 , ,; = = = β α δ δσ αβ αβ kj i g T gQ i jk ijk (20) where the heat Q and the temperature T are tensors of rank 3, but αβ g g jk , are covariant fundamental tensors. Formula (20) needs a special explanation. As known, M.Planck assumed that σ σ ≠ (v), i.e., the entropy of the system varies exclusively owing to thermodynamical processes in the object under study and is independent of its velocity relative to the observer in the laboratory reference frame [2]. As will be shown below, the law (20) agrees with the Planck statement. Further, the contraction of the heat and temperature tensors with the fundamental tensors transforms them to the vectors multiplied into scalar quantities. The latter are invariant parts of the above tensors that do not vary when passing from one reference frame to another. As to the vectors, their components are equal to unity when the moving system 4-velocity equals to zero, i.e., n=             i 1 1 1 , (21) 2 4 1 4' 3 3' 2 2' 2 4 1 1' 1 , , , 1 β β β β − + − = = = − − = n n nn nn n n n n , (22) where i is imaginary unit; , / cv = β Then the contraction in (20) of two vector quantities in indices i gives a scalar quantity, which is invariant under the Lorentz transformations. As to heat and the temperature, their invariant parts vary exclusively owing to purely thermodynamic reasons. In turn, the vector components vary exclusively, when passing from one reference frame to another. In both cases either the heat or the temperature are inversely proportional to the quantity 2 1 β − . Then the entropy will not change in the absence of heat input into the system. The latter is in a full accord with the results obtained in works [13, 14, and 15] where the temperature was shown to transform under relativistic conditions in inverse proportion to the quantity 2 1 β − . Then we can represent the temperature in Minkowski space as Τ=Τ= = i i i n g T T αβ αβ n, (23), where Τ is the invariant part of the tensor magnitude of rank 3, i.e., αβ i T . In the real space formulae (20) and (23) remain unchanged with the only difference that, first, we now use affine tensors, second, the dependences (21) and (22) take the form: n =           1 1 1 , (24) 3 3' 2 2' 2 1 1' , , 1 n nn n n n = = − = β . (25) At v =0 the spatial components of i T coincide in Euclidean space with the same components in Minkowski space. In space-time the components of squared sum of the vector quantity Τ n read 1 Year 2023 33 © 2023 Global Journals Global Journal of Science Frontier Research Volume XXIII Issue ersion I VI ( A ) The Heat Transfer by Radiation under Relativistic Conditions