PCRT.I.G.04

PCRT.I.G

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

$d Q_{N}$	$=$	$d Q_{V, N} + d Q_{S, N}$	$d Q_{N} (V, S), d Q_{V, N} (S), d Q_{S, N} (V)$
$d Q_{V, N}$	$=$	$d U_{V, N}$	$d U_{V, N} (S)$
$d Q_{S, N}$	$=$	$0$
$d W_{N}$	$=$	$d W_{V, N} + d W_{S, N}$	$d W_{N} (V, S), d W_{V, N} (S), d W_{S, N} (V)$
$d W_{V, N}$	$=$	$0$
$d W_{S, N}$	$=$	$d U_{S, N}$	$d U_{S, N} (V)$
$d U_{N}$	$=$	$d U_{V, N} + d U_{S, N}$
$U$	$=$	$\frac{3}{2} n R T_{0} {(\frac{V_{0}}{V})}^{2 / 3} \exp (\frac{2}{3} \frac{S - S_{0}}{n R})$	$U (N, V, S)$
$d Q_{N}$	$=$	$d Q_{V, N} + d Q_{p, N}$	$d Q_{N} (V, p), d Q_{V, N} (p), d Q_{p, N} (V)$
$d W_{N}$	$=$	$d W_{V, N} + d W_{p, N}$	$d W_{N} (V, p), d W_{V, N} (p), d W_{p, N} (V)$
$d Q_{V, N} + d W_{V, N}$	$=$	$d U_{V, N}$	$d U_{V, N} (p)$
$d Q_{p, N} + d W_{p, N}$	$=$	$d U_{p, N}$	$d U_{p, N} (V)$
$d U_{N}$	$=$	$d U_{V, N} + d U_{S, N}$
$1$	$=$	${(\frac{V_{0}}{V})}^{5 / 3} (\frac{p_{0}}{p}) \exp (\frac{2}{3} \frac{S (V, p) - S_{0}}{n R})$	$U (N, V, S (V, p))$
$(\frac{V}{V_{0}}) (\frac{p}{p_{0}})$	$=$	${(\frac{V_{0}}{V})}^{2 / 3} \exp (\frac{2}{3} \frac{S (V, p) - S_{0}}{n R})$	$U (N, V, S (V, p))$
$U$	$=$	$\frac{3}{2} n R T_{0} (\frac{V}{V_{0}}) (\frac{p}{p_{0}})$	$U (N, V, p)$
$Q_{V 1, N} (S_{12}, S_{11})$	$=$	$+ \frac{3}{2} n R T_{0} {(\frac{V_{0}}{V_{1}})}^{2 / 3}$
		$\times [\exp (\frac{2}{3} \frac{S_{12} - S_{0}}{n R}) - \exp (\frac{2}{3} \frac{S_{11} - S_{0}}{n R})]$	$(V, p, S : V_{1} p_{1} S_{11} \to V_{1} p_{2} S_{12}), d N = 0$
$Q_{V 1, N} (p_{2}, p_{1})$	$=$	$+ \frac{3}{2} n R T_{0} (\frac{V_{1}}{V_{0}}) [(\frac{p_{2}}{p_{0}}) - (\frac{p_{1}}{p_{0}})]$	$(V, p : V_{1} p_{1} \to V_{1} p_{2}), d N = 0$
$W_{N} (V_{2}, S_{22}, V_{1}, S_{12})$	$=$	$+ \frac{3}{2} n R T_{0} {(\frac{V_{0}}{V_{2}})}^{2 / 3} \exp (\frac{2}{3} \frac{S_{22} - S_{0}}{n R})$
		$- \frac{3}{2} n R T_{0} {(\frac{V_{0}}{V_{1}})}^{2 / 3} \exp (\frac{2}{3} \frac{S_{12} - S_{0}}{n R})$	$(V, p, S : V_{1} p_{2} S_{12} \to V_{2} p_{2} S_{22}), d N = 0$
$W_{p 2, N} (V_{2}, V_{1})$	$=$	$+ \frac{3}{2} n R T_{0} [(\frac{V_{2}}{V_{0}}) - (\frac{V_{1}}{V_{0}})] (\frac{p_{2}}{p_{0}})$	$(V, p : V_{1} p_{2} \to V_{2} p_{2}), d N = 0$
$Q_{V 2, N} (S_{21}, S_{22})$	$=$	$+ \frac{3}{2} n R T_{0} {(\frac{V_{0}}{V_{2}})}^{2 / 3}$
		$\times [\exp (\frac{2}{3} \frac{S_{21} - S_{0}}{n R}) - \exp (\frac{2}{3} \frac{S_{22} - S_{0}}{n R})]$	$(V, p, S : V_{2} p_{2} S_{22} \to V_{2} p_{1} S_{21}), d N = 0$
$Q_{V 2, N} (p_{1}, p_{2})$	$=$	$+ \frac{3}{2} n R T_{0} (\frac{V_{2}}{V_{0}}) [(\frac{p_{1}}{p_{0}}) - (\frac{p_{2}}{p_{0}})]$	$(V, p : V_{2} p_{2} \to V_{2} p_{1}), d N = 0$
$W_{N} (V_{1}, S_{11}, V_{2}, S_{21})$	$=$	$+ \frac{3}{2} n R T_{0} {(\frac{V_{0}}{V_{1}})}^{2 / 3} \exp (\frac{2}{3} \frac{S_{11} - S_{0}}{n R})$
		$- \frac{3}{2} n R T_{0} {(\frac{V_{0}}{V_{2}})}^{2 / 3} \exp (\frac{2}{3} \frac{S_{21} - S_{0}}{n R})$	$(V, p, S : V_{2} p_{1} S_{21} \to V_{1} p_{1} S_{11}), d N = 0$
$W_{p 1, N} (V_{1}, V_{2})$	$=$	$+ \frac{3}{2} n R T_{0} [(\frac{V_{1}}{V_{0}}) - (\frac{V_{2}}{V_{0}})] (\frac{p_{1}}{p_{0}})$	$(V, p : V_{2} p_{1} \to V_{1} p_{1}), d N = 0$
$0$	$=$	$Q_{V 1, N} (S_{12}, S_{11}) + W_{N} (V_{2}, S_{22}, V_{1}, S_{12})$
		$+ Q_{V 2, N} (S_{21}, S_{22}) + W_{N} (V_{1}, S_{11}, V_{2}, S_{21})$	$(V S : 111 \to 112 \to 222 \to 221 \to 111)$
$0$	$=$	$Q_{V 1, N} (p_{2}, p_{1}) + W_{p 2, N} (V_{2}, V_{1})$
		$+ Q_{V 2, N} (p_{1}, p_{2}) + W_{p 1, N} (V_{1}, V_{2})$	$(V p : 11 \to 12 \to 22 \to 21 \to 11), d N = 0$
$Q_{N}$	$=$	$Q_{N} (\to) + Q_{N} (\leftarrow)$
	$=$	$Q_{V 1, N} (S_{12}, S_{11}) + Q_{V 2, N} (S_{21}, S_{22})$
	$=$	$Q_{V 1, N} (p_{2}, p_{1}) + Q_{V 2, N} (p_{1}, p_{2})$
$W_{N}$	$=$	$W_{N} (\leftarrow) + W_{N} (\to)$
	$=$	$W_{N} (V_{2}, S_{22}, V_{1}, S_{12}) + W_{N} (V_{1}, S_{11}, V_{2}, S_{21})$
	$=$	$W_{p 2, N} (V_{2}, V_{1}) + W_{p 1, N} (V_{1}, V_{2})$

PCRT.I.G.04

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

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