PCRT.I.G.04

PCRT.I.G

04 (N,V,S(V,p))-Koordinatensystem

$\qquad \qquad$	$dQ_{N}$	$=$	$dQ_{V,N}+dQ_{S,N}$	$\qquad dQ_{N}(V,S),\,dQ_{V,N}(S),\,dQ_{S,N}(V)\qquad$
$\qquad \qquad$	$dQ_{V,N}$	$=$	$dU_{V,N}$	$\qquad dU_{V,N}(S)\qquad$
$\qquad \qquad$	$dQ_{S,N}$	$=$	$0$	$\qquad \qquad$
$\qquad \qquad$	$dW_{N}$	$=$	$dW_{V,N}+dW_{S,N}$	$\qquad dW_{N}(V,S),\,dW_{V,N}(S),\,dW_{S,N}(V)\qquad$
$\qquad \qquad$	$dW_{V,N}$	$=$	$0$	$\qquad \qquad$
$\qquad \qquad$	$dW_{S,N}$	$=$	$dU_{S,N}$	$\qquad dU_{S,N}(V)\qquad$
$\qquad \qquad$	$dU_{N}$	$=$	$dU_{V,N}+dU_{S,N}$	$\qquad \qquad$
$\qquad \qquad$	$U$	$=$	${\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V}}\right)^{2/3}\,\exp \left({\frac {2}{3}}{\frac {S-S_{0}}{n\,R}}\right)$	$\qquad U(N,V,S)\qquad$
$\qquad \qquad$	$dQ_{N}$	$=$	$dQ_{V,N}+dQ_{p,N}$	$\qquad dQ_{N}(V,p),\,dQ_{V,N}(p),\,dQ_{p,N}(V)\qquad$
$\qquad \qquad$	$dW_{N}$	$=$	$dW_{V,N}+dW_{p,N}$	$\qquad dW_{N}(V,p),\,dW_{V,N}(p),\,dW_{p,N}(V)\qquad$
$\qquad \qquad$	$dQ_{V,N}+dW_{V,N}$	$=$	$dU_{V,N}$	$\qquad dU_{V,N}(p)\qquad$
$\qquad \qquad$	$dQ_{p,N}+dW_{p,N}$	$=$	$dU_{p,N}$	$\qquad dU_{p,N}(V)\qquad$
$\qquad \qquad$	$dU_{N}$	$=$	$dU_{V,N}+dU_{S,N}$	$\qquad \qquad$
$\qquad \qquad$	$1$	$=$	$\left({\frac {V_{0}}{V}}\right)^{5/3}\left({\frac {p_{0}}{p}}\right)\,\exp \left({\frac {2}{3}}{\frac {S(V,p)-S_{0}}{n\,R}}\right)$	$\qquad U(N,V,S(V,p))\qquad$
$\qquad \qquad$	$\left({\frac {V}{V_{0}}}\right)\left({\frac {p}{p_{0}}}\right)$	$=$	$\left({\frac {V_{0}}{V}}\right)^{2/3}\,\exp \left({\frac {2}{3}}{\frac {S(V,p)-S_{0}}{n\,R}}\right)$	$\qquad U(N,V,S(V,p))\qquad$
$\qquad \qquad$	$U$	$=$	${\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V}{V_{0}}}\right)\left({\frac {p}{p_{0}}}\right)$	$\qquad U(N,V,p)\qquad$
$\qquad \qquad$	$Q_{V1,N}(S_{12},S_{11})$	$=$	$+\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	${\displaystyle }$	$\times \left[\exp \left({\frac {2}{3}}{\frac {S_{12}-S_{0}}{n\,R}}\right)-\,\exp \left({\frac {2}{3}}{\frac {S_{11}-S_{0}}{n\,R}}\right)\right]$	$\qquad (V,p,S:V_{1}p_{1}S_{11}\to V_{1}p_{2}S_{12}),\,dN=0\qquad$
$\qquad \qquad$	$Q_{V1,N}(p_{2},p_{1})$	$=$	$+\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{1}}{V_{0}}}\right)\left[\left({\frac {p_{2}}{p_{0}}}\right)-\,\left({\frac {p_{1}}{p_{0}}}\right)\right]$	$\qquad (V,p:V_{1}p_{1}\to V_{1}p_{2}),\,dN=0\qquad$
$\qquad \qquad$	$W_{N}(V_{2},S_{22},V_{1},S_{12})$	$=$	$+\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}\exp \left({\frac {2}{3}}{\frac {S_{22}-S_{0}}{n\,R}}\right)$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	${\displaystyle }$	$-\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}\exp \left({\frac {2}{3}}{\frac {S_{12}-S_{0}}{n\,R}}\right)$	$\qquad (V,p,S:V_{1}p_{2}S_{12}\to V_{2}p_{2}S_{22}),\,dN=0\qquad$
$\qquad \qquad$	$W_{p2,N}(V_{2},V_{1})$	$=$	$+\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {V_{2}}{V_{0}}}\right)-\,\left({\frac {V_{1}}{V_{0}}}\right)\right]\left({\frac {p_{2}}{p_{0}}}\right)$	$\qquad (V,p:V_{1}p_{2}\to V_{2}p_{2}),\,dN=0\qquad$
$\qquad \qquad$	$Q_{V2,N}(S_{21},S_{22})$	$=$	$+\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	${\displaystyle }$	$\times \left[\exp \left({\frac {2}{3}}{\frac {S_{21}-S_{0}}{n\,R}}\right)-\,\exp \left({\frac {2}{3}}{\frac {S_{22}-S_{0}}{n\,R}}\right)\right]$	$\qquad (V,p,S:V_{2}p_{2}S_{22}\to V_{2}p_{1}S_{21}),\,dN=0\qquad$
$\qquad \qquad$	$Q_{V2,N}(p_{1},p_{2})$	$=$	$+\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{2}}{V_{0}}}\right)\left[\left({\frac {p_{1}}{p_{0}}}\right)-\,\left({\frac {p_{2}}{p_{0}}}\right)\right]$	$\qquad (V,p:V_{2}p_{2}\to V_{2}p_{1}),\,dN=0\qquad$
$\qquad \qquad$	$W_{N}(V_{1},S_{11},V_{2},S_{21})$	$=$	$+\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}\exp \left({\frac {2}{3}}{\frac {S_{11}-S_{0}}{n\,R}}\right)$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	${\displaystyle }$	$-\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}\exp \left({\frac {2}{3}}{\frac {S_{21}-S_{0}}{n\,R}}\right)$	$\qquad (V,p,S:V_{2}p_{1}S_{21}\to V_{1}p_{1}S_{11}),\,dN=0\qquad$
$\qquad \qquad$	$W_{p1,N}(V_{1},V_{2})$	$=$	$+\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {V_{1}}{V_{0}}}\right)-\,\left({\frac {V_{2}}{V_{0}}}\right)\right]\left({\frac {p_{1}}{p_{0}}}\right)$	$\qquad (V,p:V_{2}p_{1}\to V_{1}p_{1}),\,dN=0\qquad$
$\qquad \qquad$	$0$	$=$	$Q_{V1,N}(S_{12},S_{11})+W_{N}(V_{2},S_{22},V_{1},S_{12})$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	${\displaystyle }$	$+\,Q_{V2,N}(S_{21},S_{22})+W_{N}(V_{1},S_{11},V_{2},S_{21})$	$\qquad (VS:111\to 112\to 222\to 221\to 111)\qquad$
$\qquad \qquad$	$0$	$=$	$Q_{V1,N}(p_{2},p_{1})+W_{p2,N}(V_{2},V_{1})$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	${\displaystyle }$	$+\,Q_{V2,N}(p_{1},p_{2})+W_{p1,N}(V_{1},V_{2})$	$\qquad (Vp:11\to 12\to 22\to 21\to 11),\,dN=0\qquad$
$\qquad \qquad$	$Q_{N}$	$=$	$Q_{N}(\rightarrow )+Q_{N}(\leftarrow )$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	$=$	$Q_{V1,N}(S_{12},S_{11})+Q_{V2,N}(S_{21},S_{22})$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	$=$	$Q_{V1,N}(p_{2},p_{1})+Q_{V2,N}(p_{1},p_{2})$	$\qquad \qquad$
$\qquad \qquad$	$W_{N}$	$=$	$W_{N}(\leftarrow )+W_{N}(\rightarrow )$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	$=$	$W_{N}(V_{2},S_{22},V_{1},S_{12})+W_{N}(V_{1},S_{11},V_{2},S_{21})$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	$=$	$W_{p2,N}(V_{2},V_{1})+W_{p1,N}(V_{1},V_{2})$	$\qquad \qquad$