# Page:Zur Thermodynamik bewegter Systeme (Fortsetzung).djvu/1

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Continuation

(Presented in the session of February 6, 1908.)[1]

7. Calculation of quantity H.

In order to express $H$ by the variables $U_{0}, v, \beta$, we insert the value for $p$ from (6) into (13) and obtain

 $(1-\beta^{2})\frac{\partial H}{\partial\beta}+\beta H+\beta v\left(p_{0}\frac{\partial H}{\partial U_{0}}-\frac{\partial H}{\partial v}\right)=0.$ (15)

This partial differential equation assumes a simpler form, when the quantities $\beta, v, S_{0}$ are chosen instead of $\beta, v, U_{0}$ as independent variables. Namely, $S_0$ shall be the value of entropy again, when the system is adiabatically brought to rest; of course $S = S_{0}$. Thus we think of $U_0$ as being expressed by entropy and volume; if for example

$U_{0} = F(S_{0}, v)\,$.

Then it is:

$\frac{\partial}{\partial v}-p_{0}\frac{\partial}{\partial U_{0}}=\left(\frac{\partial}{\partial v}\right)_{S_{0}}$,

because according to (7), $U_0$ is changed by $-p_{0}dv$ at adiabatic volume change. If we furthermore introduce the variable

$\varkappa=\sqrt{1-\beta^{2}}$

instead of $\beta$,

1. Compare these proceedings, CXVI, p. 1391 (1907).