Page:Zur Thermodynamik bewegter Systeme (Fortsetzung).djvu/3

 We obtain

$U=H+\beta\phi=\sqrt{1-\beta^{2}}\,U_{0}+\beta^{2}(U+pv),$|undefined

from which it is given under consideration of the first equation (14):

Finally, the momentum is according to (10):

If we summarize everything, we come to the result:

If a body whose state at rest is given by the variables $$v_{0}, U_{0}, p_{0}, T_{0}, S_{0}$$, is adiabatically brought to velocity $$\beta c$$, then the state variables assume the value:

These equations are in agreement with the results of the paper of. Besides thermodynamics, used the relativity principle, while stating equation (10) for momentum is essential in our work.