Page:Zur Thermodynamik bewegter Systeme.djvu/6

2. The differential of the supplied heated.

is increased (as the energy increase) by the performed work of the considered body, thus

$dQ=dU+pdv-\beta d\phi$^[1]

If we again introduce $U_{0},v$ and $\beta$ as independent variables, then it becomes:

$dQ={\frac {\partial \Phi }{\partial U_{0}}}dU_{0}+{\frac {\partial \Phi }{\partial v}}dv+{\frac {\partial \Phi }{\partial \beta }}d\beta --\beta \left({\frac {\partial \phi }{\partial U_{0}}}dU_{0}+{\frac {\partial \phi }{\partial v}}dv+{\frac {\partial \phi }{\partial \beta }}d\beta \right)+pdv.$

If we consider (1), (2) and (6), then it becomes:

$dQ={\frac {\partial H}{\partial U_{0}}}dU_{0}+{\frac {\partial H}{\partial v}}dv+\left(p_{0}{\frac {\partial H}{\partial U_{0}}}-{\frac {\partial H}{\partial v}}\right)dv,$

or

$dQ={\frac {\partial H}{\partial U_{0}}}(dU_{0}+p_{0}dv).$

(7)

This expression is valid in full generality.

3. The temperature of the moving body.

We first consider a system of bodies, all of them moving with the same constant velocity. Experience tells us that $dQ/T$ is then a complete differential. Equation (7) shows that this condition is satisfied, when we put

$T=T_{0}{\frac {\partial H}{\partial U_{0}}}\cdot f(\beta )$

(8a)

$T_{0}$ is the integrating denominator of $dU_{0}+p_{0}dv$, when we (analogous to the preceding) understand under $T_{0}$ the temperature assumed by the body when it is adiabatically

1. Planck was the first who alluded to the fact, that the translation work $\beta d\phi$ must be considered in the determination of the temperature of a moving cavity.