We obtain

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

(17) |

Finally, the momentum is according to (10):

(18) |

If we summarize everything, we come to the result:

If a body whose state at rest is given by the variables , is adiabatically brought to velocity , then the state variables assume the value:

(14) |

(14) |

(17) |

(16) |

(18) |

These equations are in agreement with the results of the paper of Planck^{[1]}. Besides thermodynamics, Planck used the relativity principle, while stating equation (10) for momentum is essential in our work.

- ↑ Berliner Berichte, 1907, p. 542.