Page:Zur Thermodynamik bewegter Systeme.djvu/8

because the ordinary definition of temperature must hold for bodies of same velocity, so the form for $\phi$ is given by

$\phi (T,\beta )=T\cdot g(\beta ).$

We want to set this function $g(\beta )$, as well as function $f(\beta )$ in (8a), equal to one; then it becomes

$T=T_{0}{\frac {\partial H}{\partial U_{0}}}.$

(8)

Though we have to emphasize, that there is a certain arbitrariness in this. Even when we don't set these functions equal to one, we neither come into contradiction with the theorem of the impossibility of a thermal perpetual motion machine, nor with the ordinary definition of temperature which is indeed only related to bodies of same velocity. The criterion of equality of temperature is not applicable to bodies of unequal velocity, since we cannot directly bring them in reversible heat exchange, but only with the aid of an auxiliary body which assumes different velocities. Though if we don't set $g(\beta )$ equal to one, then also the entropy of the adiabatic acceleration changes.

Anyway, it is the easiest way to define $T$ by equation (8); then $dQ/T$ is a complete differential and the entropy remains constant at adiabatic acceleration.^[1]

4. The entropy of a moving body.

We arrived at the result that pressure and temperature assume the values

$p=p_{0}{\frac {\partial H}{\partial H_{0}}}-{\frac {\partial H}{\partial v}},$

(6)

$T=T_{0}{\frac {\partial H}{\partial U_{0}}}$

(8)

at isochoric-adiabatic acceleration.

1. This was also concluded in the papers of v. Mosengeil and Planck at the determination of the temperature of a moving cavity.