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PCRT.I.G.02
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PCRT.I.G
02 (N,p,S)-Koordinatensystem
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{\displaystyle \qquad \qquad }
d
Q
N
{\displaystyle dQ_{N}}
=
{\displaystyle =}
d
Q
p
,
N
+
d
Q
S
,
N
{\displaystyle dQ_{p,N}+dQ_{S,N}}
d
Q
N
(
p
,
S
)
,
d
Q
p
,
N
(
S
)
,
d
Q
S
,
N
(
p
)
{\displaystyle \qquad dQ_{N}(p,S),\,dQ_{p,N}(S),\,dQ_{S,N}(p)\qquad }
{\displaystyle \qquad \qquad }
d
Q
p
,
N
{\displaystyle dQ_{p,N}}
=
{\displaystyle =}
d
H
p
,
N
{\displaystyle dH_{p,N}}
d
H
p
,
N
(
S
)
{\displaystyle \qquad dH_{p,N}(S)\qquad }
{\displaystyle \qquad \qquad }
d
Q
S
,
N
{\displaystyle dQ_{S,N}}
=
{\displaystyle =}
0
{\displaystyle 0}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
d
W
N
{\displaystyle dW_{N}}
=
{\displaystyle =}
d
W
p
,
N
+
d
W
S
,
N
{\displaystyle dW_{p,N}+dW_{S,N}}
d
W
N
(
p
,
S
)
,
d
W
p
,
N
(
S
)
,
d
W
S
,
N
(
p
)
{\displaystyle \qquad dW_{N}(p,S),\,dW_{p,N}(S),\,dW_{S,N}(p)\qquad }
{\displaystyle \qquad \qquad }
d
W
p
,
N
{\displaystyle dW_{p,N}}
=
{\displaystyle =}
d
U
p
,
N
−
d
H
p
,
N
{\displaystyle dU_{p,N}-dH_{p,N}}
d
U
p
,
N
(
S
)
{\displaystyle \qquad dU_{p,N}(S)\qquad }
{\displaystyle \qquad \qquad }
d
W
S
,
N
{\displaystyle dW_{S,N}}
=
{\displaystyle =}
d
U
S
,
N
{\displaystyle dU_{S,N}}
d
U
S
,
N
(
p
)
{\displaystyle \qquad dU_{S,N}(p)\qquad }
{\displaystyle \qquad \qquad }
d
U
N
{\displaystyle dU_{N}}
=
{\displaystyle =}
d
U
p
,
N
+
d
U
S
,
N
{\displaystyle dU_{p,N}+dU_{S,N}}
d
U
N
(
p
,
S
)
{\displaystyle \qquad dU_{N}(p,S)\qquad }
{\displaystyle \qquad \qquad }
H
{\displaystyle H}
=
{\displaystyle =}
+
5
2
n
R
T
0
(
p
p
0
)
2
/
5
exp
(
2
5
S
−
S
0
n
R
)
{\displaystyle +\,{\frac {5}{2}}\,n\,R\,T_{0}\,\left({\frac {p}{p_{0}}}\right)^{2/5}\,\exp \left({\frac {2}{5}}{\frac {S-S_{0}}{n\,R}}\right)}
H
(
N
,
p
,
S
)
{\displaystyle \qquad H(N,p,S)\qquad }
{\displaystyle \qquad \qquad }
U
{\displaystyle U}
=
{\displaystyle =}
+
3
2
n
R
T
0
(
p
p
0
)
2
/
5
exp
(
2
5
S
−
S
0
n
R
)
{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {p}{p_{0}}}\right)^{2/5}\,\exp \left({\frac {2}{5}}{\frac {S-S_{0}}{n\,R}}\right)}
U
(
N
,
p
,
S
)
{\displaystyle \qquad U(N,p,S)\qquad }
{\displaystyle \qquad \qquad }
Q
p
1
,
N
(
S
2
,
S
1
)
{\displaystyle Q_{p1,N}(S_{2},S_{1})}
=
{\displaystyle =}
+
5
2
n
R
T
0
(
p
1
p
0
)
2
/
5
[
exp
(
2
5
S
2
n
R
)
−
exp
(
2
5
S
1
n
R
)
]
{\displaystyle +\,{\frac {5}{2}}\,n\,R\,T_{0}\,\left({\frac {p_{1}}{p_{0}}}\right)^{2/5}\,\left[\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)\right]}
(
p
,
S
:
p
1
S
1
→
p
1
S
2
)
,
d
N
=
0
{\displaystyle \qquad (p,S:p_{1}S_{1}\to p_{1}S_{2}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
W
p
1
,
N
(
S
2
,
S
1
)
{\displaystyle W_{p1,N}(S_{2},S_{1})}
=
{\displaystyle =}
−
n
R
T
0
(
p
1
p
0
)
2
/
5
[
exp
(
2
5
S
2
n
R
)
−
exp
(
2
5
S
1
n
R
)
]
{\displaystyle -\,n\,R\,T_{0}\,\left({\frac {p_{1}}{p_{0}}}\right)^{2/5}\,\left[\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)\right]}
(
p
,
S
:
p
1
S
1
→
p
1
S
2
)
,
d
N
=
0
{\displaystyle \qquad (p,S:p_{1}S_{1}\to p_{1}S_{2}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
W
S
2
,
N
(
p
2
,
p
1
)
{\displaystyle W_{S2,N}(p_{2},p_{1})}
=
{\displaystyle =}
+
3
2
n
R
T
0
[
(
p
2
p
0
)
2
/
5
−
(
p
1
p
0
)
2
/
3
]
exp
(
2
5
S
2
−
S
0
n
R
)
{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}-\,\left({\frac {p_{1}}{p_{0}}}\right)^{2/3}\right]\,\exp \left({\frac {2}{5}}{\frac {S_{2}-S_{0}}{n\,R}}\right)}
(
p
,
S
:
p
1
S
2
→
p
2
S
2
)
,
d
N
=
0
{\displaystyle \qquad (p,S:p_{1}S_{2}\to p_{2}S_{2}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
Q
p
2
,
N
(
S
1
,
S
2
)
{\displaystyle Q_{p2,N}(S_{1},S_{2})}
=
{\displaystyle =}
+
5
2
n
R
T
0
(
p
2
p
0
)
2
/
5
[
exp
(
2
5
S
1
n
R
)
−
exp
(
2
5
S
2
n
R
)
]
{\displaystyle +\,{\frac {5}{2}}\,n\,R\,T_{0}\,\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}\,\left[\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)\right]}
(
p
,
S
:
p
2
S
2
→
p
2
S
1
)
,
d
N
=
0
{\displaystyle \qquad (p,S:p_{2}S_{2}\to p_{2}S_{1}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
W
p
2
,
N
(
S
1
,
S
2
)
{\displaystyle W_{p2,N}(S_{1},S_{2})}
=
{\displaystyle =}
−
n
R
T
0
(
p
2
p
0
)
2
/
5
[
exp
(
2
5
S
1
n
R
)
−
exp
(
2
5
S
2
n
R
)
]
{\displaystyle -\,n\,R\,T_{0}\,\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}\,\left[\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)\right]}
(
p
,
S
:
p
2
S
2
→
p
2
S
1
)
,
d
N
=
0
{\displaystyle \qquad (p,S:p_{2}S_{2}\to p_{2}S_{1}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
W
S
1
,
N
(
p
1
,
p
2
)
{\displaystyle W_{S1,N}(p_{1},p_{2})}
=
{\displaystyle =}
+
3
2
n
R
T
0
[
(
p
1
p
0
)
2
/
5
−
(
p
2
p
0
)
2
/
5
]
exp
(
2
5
S
1
−
S
0
n
R
)
{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {p_{1}}{p_{0}}}\right)^{2/5}-\,\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}\right]\,\exp \left({\frac {2}{5}}{\frac {S_{1}-S_{0}}{n\,R}}\right)}
(
p
,
S
:
p
2
S
1
→
p
1
S
1
)
,
d
N
=
0
{\displaystyle \qquad (p,S:p_{2}S_{1}\to p_{1}S_{1}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
0
{\displaystyle 0}
=
{\displaystyle =}
Q
p
1
,
N
(
S
2
,
S
1
)
+
W
p
1
,
N
(
S
2
,
S
1
)
+
W
S
2
,
N
(
p
2
,
p
1
)
{\displaystyle Q_{p1,N}(S_{2},S_{1})+W_{p1,N}(S_{2},S_{1})+W_{S2,N}(p_{2},p_{1})}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
{\displaystyle }
{\displaystyle }
+
Q
p
2
,
N
(
S
1
,
S
2
)
+
W
p
2
,
N
(
S
1
,
S
2
)
+
W
S
1
,
N
(
p
1
,
p
2
)
{\displaystyle +\,Q_{p2,N}(S_{1},S_{2})+\,W_{p2,N}(S_{1},S_{2})+W_{S1,N}(p_{1},p_{2})}
(
p
S
:
11
→
12
→
22
→
21
→
11
)
,
d
N
=
0
{\displaystyle \qquad (pS:11\to 12\to 22\to 21\to 11),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
Q
N
{\displaystyle Q_{N}}
=
{\displaystyle =}
Q
N
(
→
)
+
Q
N
(
←
)
{\displaystyle Q_{N}(\rightarrow )+Q_{N}(\leftarrow )}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
{\displaystyle }
=
{\displaystyle =}
+
5
2
n
R
T
0
[
(
p
1
p
0
)
2
/
5
−
(
p
2
p
0
)
2
/
5
]
{\displaystyle +\,{\frac {5}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {p_{1}}{p_{0}}}\right)^{2/5}-\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}\right]}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
{\displaystyle }
{\displaystyle }
×
[
exp
(
2
5
S
2
n
R
)
−
exp
(
2
5
S
1
n
R
)
]
{\displaystyle \times \,\left[\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)\right]}
(
p
S
:
11
→
12
→
22
→
21
→
11
)
,
d
N
=
0
{\displaystyle \qquad (pS:11\to 12\to 22\to 21\to 11),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
W
N
{\displaystyle W_{N}}
=
{\displaystyle =}
W
N
(
←
)
+
W
N
(
→
)
{\displaystyle W_{N}(\leftarrow )+W_{N}(\rightarrow )}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
{\displaystyle }
=
{\displaystyle =}
−
5
2
n
R
T
0
[
(
p
1
p
0
)
2
/
5
−
(
p
2
p
0
)
2
/
5
]
{\displaystyle -\,{\frac {5}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {p_{1}}{p_{0}}}\right)^{2/5}-\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}\right]}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
{\displaystyle }
{\displaystyle }
×
[
exp
(
2
5
S
2
n
R
)
−
exp
(
2
5
S
1
n
R
)
]
{\displaystyle \times \,\left[\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)\right]}
(
p
S
:
11
→
12
→
22
→
21
→
11
)
,
d
N
=
0
{\displaystyle \qquad (pS:11\to 12\to 22\to 21\to 11),\,dN=0\qquad }
![{\displaystyle +\,{\frac {5}{2}}\,n\,R\,T_{0}\,\left({\frac {p_{1}}{p_{0}}}\right)^{2/5}\,\left[\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1d8d49996f43de6646bb185746019dc25f1f6857)
![{\displaystyle -\,n\,R\,T_{0}\,\left({\frac {p_{1}}{p_{0}}}\right)^{2/5}\,\left[\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/182bed1330681f35f842d63259a267d7460ff85a)
![{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}-\,\left({\frac {p_{1}}{p_{0}}}\right)^{2/3}\right]\,\exp \left({\frac {2}{5}}{\frac {S_{2}-S_{0}}{n\,R}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44589e8036060bf9101f26cbc107b7f22c04dd3d)
![{\displaystyle +\,{\frac {5}{2}}\,n\,R\,T_{0}\,\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}\,\left[\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/359fb2fc5d6119dcb7cbdd1b6ebc648feb87a26f)
![{\displaystyle -\,n\,R\,T_{0}\,\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}\,\left[\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c109ebea7e26c33952011f51da0232cefcfd0b13)
![{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {p_{1}}{p_{0}}}\right)^{2/5}-\,\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}\right]\,\exp \left({\frac {2}{5}}{\frac {S_{1}-S_{0}}{n\,R}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ade89a8193f4cb7f711d7699879aff74de4e6a7b)
![{\displaystyle +\,{\frac {5}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {p_{1}}{p_{0}}}\right)^{2/5}-\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9aff82ee632662b34232ba368a4aaaa1ecc65ed)
![{\displaystyle \times \,\left[\exp \left({\frac {2}{5}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{5}}{\frac {S_{1}}{n\,R}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2421a61bb375d5a08b9984ce02bad0315e3afc9e)
![{\displaystyle -\,{\frac {5}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {p_{1}}{p_{0}}}\right)^{2/5}-\left({\frac {p_{2}}{p_{0}}}\right)^{2/5}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/71c5ce4353457645b9e284a18ae1f0bb9fa3ac7e)
