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. 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 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 $$q = \beta c$$, 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

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

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

Furthermore, we introduce the quantity

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