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

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

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

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:

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

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

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

instead of $$\beta$$,