24 Adding Energy means Adding Momentum and Kinetic Energy
In STR, relativ velocity v is supposed to be constant. Therefore the Epstein angle φ with sin(φ) = v / c is constant, too. The energy-momentum diagram shows clearly that any increase ΔE of the rest energy E goes along with an increase Δp of momentum:
If some energy is added to E then E' j= E / √ and p will increase ! In another paper we have worked out that in STR kinetic energy and momentum are proportional to each other if the relative velocity v remains constant:
So we have to investigate how to split ΔE' jinto an increase of the heat content jof the gas and an increase of the kinetic energy jof the gas. Eddington
[4, p. 34] and others oversimplify the situation if they directly deduce ΔQ' = ΔQ / √ from ΔE' = ΔE / √ . It is wrong to interpret the total increase ΔE' as an increase of thermal energy - there is always an increase of kinetic energy, too.