T24   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.

Components of Rest Energy First Law of Thermodynamics