CPRT.I.F.01

CPRT.I.F

01 (N,V,S)-Koordinatensystem

$$	$d{Q}_N$	$=$	$d{Q}_{V,N}+d{Q}_{S,N}$	$d{Q}_N(V,S),d{Q}_{V,N}(S),d{Q}_{S,N}(V)$
$$	$d{Q}_{V,N}$	$=$	$d{U}_{V,N}$	$d{U}_{V,N}(S)$
$$	$d{Q}_{S,N}$	$=$	$0$	$$
$$	$d{W}_N$	$=$	$d{W}_{V,N}+d{W}_{S,N}$	$d{W}_N(V,S),d{W}_{V,N}(S),d{W}_{S,N}(V)$
$$	$d{W}_{V,N}$	$=$	$0$	$$
$$	$d{W}_{S,N}$	$=$	$d{U}_{S,N}$	$d{U}_{S,N}(V)$
$$	$d{U}_N$	$=$	$d{U}_{V,N}+d{U}_{S,N}$	$$
$$	$U$	$=$	$\frac{3}{2}nR{T}_0{\left(\frac{V_0}{V}\right)}^{2/3}\exp \left(\frac{2}{3}\frac{S-S_0}{nR}\right)$	$U(N,V,S)$
$$	$Q_{V1,N}(S_2,S_1)$	$=$	$+\frac{3}{2}nR{T}_0{\left(\frac{V_0}{V_1}\right)}^{2/3}[\exp \left(\frac{2}{3}\frac{S_2}{nR}\right)-\exp \left(\frac{2}{3}\frac{S_1}{nR}\right)]$	$(V,S:V_1{S}_1\to V_1{S}_2),dN=0$
$$	$W_{S2,N}(V_2,V_1)$	$=$	$+\frac{3}{2}nR{T}_0[{\left(\frac{V_0}{V_2}\right)}^{2/3}-{\left(\frac{V_0}{V_1}\right)}^{2/3}]\exp \left(\frac{2}{3}\frac{S_2-S_0}{nR}\right)$	$(V,S:V_1{S}_2\to V_2{S}_2),dN=0$
$$	$Q_{V2,N}(S_1,S_2)$	$=$	$+\frac{3}{2}nR{T}_0{\left(\frac{V_0}{V_2}\right)}^{2/3}[\exp \left(\frac{2}{3}\frac{S_1}{nR}\right)-\exp \left(\frac{2}{3}\frac{S_2}{nR}\right)]$	$(V,S:V_2{S}_2\to V_2{S}_1),dN=0$
$$	$W_{S1,N}(V_1,V_2)$	$=$	$+\frac{3}{2}nR{T}_0[{\left(\frac{V_0}{V_1}\right)}^{2/3}-{\left(\frac{V_0}{V_2}\right)}^{2/3}]\exp \left(\frac{2}{3}\frac{S_1-S_0}{nR}\right)$	$(V,S:V_2{S}_1\to V_1{S}_1),dN=0$
$$	$0$	$=$	$Q_{V1,N}(S_2,S_1)+W_{S2,N}(V_2,V_1)$	$$
$$	${\displaystyle }$	${\displaystyle }$	$+Q_{V2,N}(S_1,S_2)+W_{S1,N}(V_1,V_2)$	$(VS:11\to 12\to 22\to 21\to 11),dN=0$
$$	$Q_N$	$=$	$Q_N(\to )+Q_N(\leftarrow )$	$$
$$	${\displaystyle }$	$=$	$+\frac{3}{2}nR{T}_0[{\left(\frac{V_0}{V_1}\right)}^{2/3}-{\left(\frac{V_0}{V_2}\right)}^{2/3}]$	$$
$$	${\displaystyle }$	${\displaystyle }$	$\times [\exp \left(\frac{2}{3}\frac{S_2}{nR}\right)-\exp \left(\frac{2}{3}\frac{S_1}{nR}\right)]$	$(VS:11\to 12\to 22\to 21\to 11),dN=0$
$$	$W_N$	$=$	$W_N(\leftarrow )+W_N(\to )$	$$
$$	${\displaystyle }$	$=$	$-\frac{3}{2}nR{T}_0[{\left(\frac{V_0}{V_1}\right)}^{2/3}-{\left(\frac{V_0}{V_2}\right)}^{2/3}]$	$$
$$	${\displaystyle }$	${\displaystyle }$	$\times [\exp \left(\frac{2}{3}\frac{S_2}{nR}\right)-\exp \left(\frac{2}{3}\frac{S_1}{nR}\right)]$	$(VS:11\to 12\to 22\to 21\to 11),dN=0$