PCRT.I.G.03

PCRT.I.G

03 (N,V,T)-Koordinatensystem

$\qquad \qquad$	$dQ_{N}$	$=$	$dQ_{V,N}+dQ_{T,N}$	$\qquad dQ_{N}(V,T)\qquad$
$\qquad \qquad$	$dQ_{V,N}$	$=$	$dU_{V,N}$	$\qquad dU_{V,N}(T)\qquad$
$\qquad \qquad$	$dQ_{T,N}$	$=$	$dU_{T,N}-dF_{T,N}$	$\qquad dU_{T,N}(V),\,dF_{T,N}(V)\qquad$
$\qquad \qquad$	$dW_{N}$	$=$	$dW_{V,N}+dW_{T,N}$	$\qquad dW_{N}(V,T),\,dW_{V,N}(T),\,dW_{T,N}(V)\qquad$
$\qquad \qquad$	$dW_{V,N}$	$=$	$0$	$\qquad \qquad$
$\qquad \qquad$	$dW_{T,N}$	$=$	$dF_{T,N}$	$\qquad \qquad$
$\qquad \qquad$	$dU_{N}$	$=$	$dU_{V,N}+dU_{T,N}$	$\qquad dU_{N}(V,T)\qquad$
$\qquad$	$F$	$=$	$-\,n\,R\,T-\,{\frac {3}{2}}\,n\,R\,T\,\ln \left({\frac {T}{T_{0}}}\right)-\,n\,R\,T\,\ln \left({\frac {V}{V_{0}}}\right)$	$\qquad F(N,V,T)\qquad$
$\qquad \qquad$	$U$	$=$	$+\,{\frac {3}{2}}\,n\,R\,T$	$\qquad U(N,V,T)\qquad$
$\qquad \qquad$	$Q_{V1,N}(T_{2},T_{1})$	$=$	${\frac {3}{2}}\,n\,R\,(T_{2}-T_{1})$	$\qquad (V,T:V_{1}T_{1}\to V_{1}T_{2}),\,dN=0\qquad$
$\qquad \qquad$	$Q_{T2,N}(V_{2},V_{1})$	$=$	$+\,n\,R\,T_{2}\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\right]$	$\qquad (V,T:V_{1}T_{2}\to V_{2}T_{2}),\,dN=0\qquad$
$\qquad \qquad$	$W_{T2,N}(V_{2},V_{1})$	$=$	$-\,n\,R\,T_{2}\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\right]$	$\qquad (V,T:V_{1}T_{2}\to V_{2}T_{2}),\,dN=0\qquad$
$\qquad \qquad$	$Q_{V2,N}(T_{1},T_{2})$	$=$	${\frac {3}{2}}\,n\,R\,(T_{1}-T_{2})$	$\qquad (V,T:V_{2}T_{2}\to V_{2}T_{1}),\,dN=0\qquad$
$\qquad \qquad$	$Q_{T1,N}(V_{1},V_{2})$	$=$	$+\,n\,R\,T_{1}\,\left[\ln {\frac {V_{1}}{V_{0}}}-\ln {\frac {V_{2}}{V_{0}}}\right]$	$\qquad (V,T:V_{2}T_{1}\to V_{1}T_{1}),\,dN=0\qquad$
$\qquad \qquad$	$W_{T1,N}(V_{1},V_{2})$	$=$	$-\,n\,R\,T_{1}\,\left[\ln {\frac {V_{1}}{V_{0}}}-\ln {\frac {V_{2}}{V_{0}}}\right]$	$\qquad (V,T:V_{2}T_{1}\to V_{1}T_{1}),\,dN=0\qquad$
$\qquad \qquad$	$0$	$=$	$Q_{V1,N}(T_{2},T_{1})+Q_{T2,N}(V_{2},V_{1})+W_{T2,N}(V_{2},V_{1})$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	${\displaystyle }$	$+\,Q_{V2,N}(T_{1},T_{2})+W_{T1,N}(V_{1},V_{2})+W_{T1,N}(V_{1},V_{2})$	$\qquad (VS:11\to 12\to 22\to 21\to 11),\,dN=0\qquad$
$\qquad \qquad$	$Q_{N}$	$=$	$Q_{N}(\rightarrow )+Q_{N}(\leftarrow )$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	$=$	$+\,n\,R\,(T_{2}-T_{1})\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\right]$	$\qquad (VS:11\to 12\to 22\to 21\to 11),\,dN=0\qquad$
$\qquad \qquad$	$W_{N}$	$=$	$W_{N}(\leftarrow )+W_{N}(\rightarrow )$	$\qquad \qquad$
$\qquad \qquad$	${\displaystyle }$	$=$	$-\,n\,R\,(T_{2}-T_{1})\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\right]$	$\qquad (VS:11\to 12\to 22\to 21\to 11),\,dN=0\qquad$