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

( ) 2 3 1 2 2 2 1 2 0 238 .0 208 .0 1 TaT TaT V E Λ + = − = β ε . (40) If the velocity v =0, we have from (40): ( ) Λ + = 238 .0 208 .0 4 0 0 aT ε , (41) but after this condition we must have 0,208 + 0,238 1 =Λ according to Stefan-Boltzmann’s law. Then 33.3 =Λ and ( ) ( ) ( ) ( ) ( ) 2 20 3 10 2 2 20 2 10 2 3 1 2 2 2 1 2 0 0 1 792 .0 1 208 .0 792 .0 208 .0 1 β β β ε − + − = + = − = T T T T TT TaT V E (42) for the energy density of radiation under relativistic conditions. Now we show that the condition (37) is met, i.e., that quantity ϑ is near to zero and much less than ( ) [ ] ∞→ = +− +− y y y e y ϑ 1 ln . First, we should solve a transcendent equation ( ) ϑ ϑ e +− −= =Λ 1 ln 22.7 , (43) its solution (see Appendix below) is: ) 1ln( Λ− − −= e ϑ . (44) and .33.3 0416 .0 << ≈ ϑ As we see, condition (37) is full met. III. D iscussion It should be noted at once that the dependence (42) does not lead to the point of absurdity and contradictions. The dependence (42) provides rather a probable answer to the question concerning the temperature transformation under relativistic conditions. It is evident that the dependence (1) is incorrect and would be rejected many years ago and without all mathematical involvements if it were not a giant authority of Planck and Einstein. Really, how is the dependence (1) be followed if such cosmic objects as quasars do exist, whose velocity v of motion can be equal 0,93 c with the luminosity reaching enormous values? The first principle of thermodynamics leads to the point of absurdity under relativistic conditions if one considers that the temperature of the object under study varies with proportion to 2 2 1 c v − as c v → . Indeed, in order to obtain the Lorentz transformation from the first principle of thermodynamics we have to express the heat throw the temperature, i.e., TdS dQ = or . SdT dQ = The entropy is a Lorentz invariant, i.e., 0 S S = . If we did not input the heat in the studied system accelerating it up to speed v , then 0 = TdS and the quantity T disappears from the equation. Only the term . SdT gives us the result; it is . 1/ 2 0 β − = TT However, e.g., Einstein [8], uses the expression 2 0 1 β − = QQ and it means that 0 . 1 2 0 ≠ − = β TT as 0 S S = . It is a nonsense. In the most general case the temperature is a complex mathematical object. It comprises an invariant part independent of the motion velocity and a part dependent on the velocity and oriented in space. Under normal conditions the temperature becomes a scalar, the same does for the heat. The entropy problem has not been studied completely. It is not improbable that the entropy can be a tensor object in which indices are contracted which results in a scalar independent of the system motion velocity. Evidently, it is for experiment to solve this problem. However no experiment has been performed since the birth of relativistic thermodynamics in 1907. Of course, the law (20) requires justification at the molecular level, however it is other problem. Having obtained the above results, we can now make important conclusions concerning relativistic thermodynamics as a whole. First of all, they concern a relativistic temperature T . Taking into consideration the above results and results obtained in [3, 13-15, 18 - 23], we can now contend with a high degree of probability: © 2023 Global Journals 1 Year 2023 36 Global Journal of Science Frontier Research Volume XXIII Issue ersion I VI ( A ) The Heat Transfer by Radiation under Relativistic Conditions