Page:Zur Thermodynamik bewegter Systeme.djvu/13

 when

(the latter relation generally holds for adiabatic state changes, according to (7)).

We notice that according to (10) and (2)

$\begin{array}{rl} H= & U-\beta\phi=U-q\mathfrak{G}=U-\beta^{2}(pv+U)\\ = & U(1-\beta^{2})-\beta^{2}pv\end{array}$

If we also insert for $$U$$ its value from (5), then it is given

$H=(1-\beta^{2})H-(1-\beta^{2})\beta\frac{\partial H}{\partial\beta}-\beta^{2}pv$

or

Then it is

If we insert this value into (11) and consider (12), then we see that indeed $$dp=0$$.

The simultaneous change of $$T$$ is: