Page:Zur Thermodynamik bewegter Systeme.djvu/2

In the present paper I have attempted to work out a theory of an arbitrarily moving body as well. The chosen way differs essentially from the method of Planck. Only the thermodynamic theorems as well as the definition of electromagnetic momentum are presupposed. If one then requires that a co-moving observer shall not notice his motion, then the Fitzgerald-Lorentz contraction hypothesis is given.

Thus we consider an arbitrary body, whose state is given by the inner energy $U_{0}$ and the volume $v$ when at rest. If it is adiabatically brought to the velocity $q=\beta c$,^[1] then it has the specific momentum ${\mathfrak {G}}$ which must be representable as a function of $U_{0},v,\beta$. We put

${\mathfrak {G}}={\frac {1}{c}}\phi (U_{0},v,\beta ).$

There, the performed work of the translation forces is

$\int q\ dt{\frac {d{\mathfrak {G}}}{dt}}=\int _{0}^{\beta }\beta {\frac {\partial \phi }{\partial \beta }}d\beta .$

The energy of the body has increased by this amount; if we denote it by $U$, then

$U=U_{0}+\int _{0}^{\beta }\beta {\frac {\partial \phi }{\partial \beta }}d\beta =\Phi (U_{0},v,\beta ),$ ${\frac {\partial \Phi }{\partial \beta }}=\beta {\frac {\partial \phi }{\partial \beta }}.$

(1)

Furthermore, we introduce the quantity

$H=U-\beta \phi \,$,

(2)

that we can also consider as function of $U_{0},v$ and $\beta$. Then it is:

1. Only reversible processes shall be discussed, $c$ is the speed of light in the aether.