Mechanisches Gleichgewicht und Druck

• Trennung diathermisch und beweglich
• $S=S^{\left(1\right)}\left(U^{\left(1\right)},V^{\left(1\right)},N^{\left(1\rig... ...(2\right)}\left(U^{\left(2\right)},V^{\left(2\right)},N^{\left(2\right)}\right)$
• Nebenbedinungen
  • $d\left(V^{\left(1\right)}+V^{\left(2\right)}\right)=0\Rightarrow dV^{\left(1\right)}=-dV^{\left(2\right)}$
  • $dN^{\left(1\right)}=dN^{\left(2\right)}=0$
  • $d\left(U^{\left(1\right)}+U^{\left(2\right)}\right)=0\Rightarrow dU^{\left(1\right)}=-dU^{\left(2\right)}$
• Notwendig für neues Exremum
  $$dS=0={\scriptstyle \left(\frac{1}{T^{\left(1\right)}}-\frac{1}{T^... ...ght)}}-\frac{p^{\left(2\right)}}{T^{\left(2\right)}}\right)dV^{\left(1\right)}}$$

• Lösungsansatz
  

  $${\scriptstyle T^{\left(1\right)}\left(U^{\left(1\right)},V^{\left(1\right)},N^{\left(1\right)}\right)} = {\scriptstyle T^{\left(2\right)}\left(U-U^{\left(1\right)},V-V^{\left(1\right)},N^{\left(2\right)}\right)}$$

  $${\scriptstyle p^{\left(1\right)}\left(U^{\left(1\right)},V^{\left(1\right)},N^{\left(1\right)}\right)} = {\scriptstyle p^{\left(2\right)}\left(U-U^{\left(1\right)},V-V^{\left(1\right)},N^{\left(2\right)}\right)}$$

  
  $U^{\left(1\right)},V^{\left(1\right)}$ sind die Unbekannten $\Rightarrow$ Lösen