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1
01 (N,V,S)-Koordinatensystem
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<
PCRT
|
I
< Anhang A2: Formelsammlung Kreisprozesse - PCRT/I/df3a
01 (N,V,S)-Koordinatensystem
[
Bearbeiten
]
{\displaystyle \qquad \qquad }
d
Q
N
{\displaystyle dQ_{N}}
=
{\displaystyle =}
d
Q
V
,
N
+
d
Q
S
,
N
{\displaystyle dQ_{V,N}+dQ_{S,N}}
d
Q
N
(
V
,
S
)
,
d
Q
V
,
N
(
S
)
,
d
Q
S
,
N
(
V
)
{\displaystyle \qquad dQ_{N}(V,S),\,dQ_{V,N}(S),\,dQ_{S,N}(V)\qquad }
{\displaystyle \qquad \qquad }
d
Q
V
,
N
{\displaystyle dQ_{V,N}}
=
{\displaystyle =}
d
U
V
,
N
{\displaystyle dU_{V,N}}
d
U
V
,
N
(
S
)
{\displaystyle \qquad dU_{V,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
V
,
N
+
d
W
S
,
N
{\displaystyle dW_{V,N}+dW_{S,N}}
d
W
N
(
V
,
S
)
,
d
W
V
,
N
(
S
)
,
d
W
S
,
N
(
V
)
{\displaystyle \qquad dW_{N}(V,S),\,dW_{V,N}(S),\,dW_{S,N}(V)\qquad }
{\displaystyle \qquad \qquad }
d
W
V
,
N
{\displaystyle dW_{V,N}}
=
{\displaystyle =}
0
{\displaystyle 0}
{\displaystyle \qquad \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
(
V
)
{\displaystyle \qquad dU_{S,N}(V)\qquad }
{\displaystyle \qquad \qquad }
d
U
N
{\displaystyle dU_{N}}
=
{\displaystyle =}
d
U
V
,
N
+
d
U
S
,
N
{\displaystyle dU_{V,N}+dU_{S,N}}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
U
{\displaystyle U}
=
{\displaystyle =}
3
2
n
R
T
0
(
V
0
V
)
2
/
3
exp
(
2
3
S
−
S
0
n
R
)
{\displaystyle {\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)}
U
(
N
,
V
,
S
)
{\displaystyle \qquad U(N,V,S)\qquad }
{\displaystyle \qquad \qquad }
Q
V
1
,
N
(
S
2
,
S
1
)
{\displaystyle Q_{V1,N}(S_{2},S_{1})}
=
{\displaystyle =}
+
3
2
n
R
T
0
(
V
0
V
1
)
2
/
3
[
exp
(
2
3
S
2
n
R
)
−
exp
(
2
3
S
1
n
R
)
]
{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}\,\left[\exp \left({\frac {2}{3}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{3}}{\frac {S_{1}}{n\,R}}\right)\right]}
(
V
,
S
:
V
1
S
1
→
V
1
S
2
)
,
d
N
=
0
{\displaystyle \qquad (V,S:V_{1}S_{1}\to V_{1}S_{2}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
W
S
2
,
N
(
V
2
,
V
1
)
{\displaystyle W_{S2,N}(V_{2},V_{1})}
=
{\displaystyle =}
+
3
2
n
R
T
0
[
(
V
0
V
2
)
2
/
3
−
(
V
0
V
1
)
2
/
3
]
exp
(
2
3
S
2
−
S
0
n
R
)
{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}-\,\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}\right]\,\exp \left({\frac {2}{3}}{\frac {S_{2}-S_{0}}{n\,R}}\right)}
(
V
,
S
:
V
1
S
2
→
V
2
S
2
)
,
d
N
=
0
{\displaystyle \qquad (V,S:V_{1}S_{2}\to V_{2}S_{2}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
Q
V
2
,
N
(
S
1
,
S
2
)
{\displaystyle Q_{V2,N}(S_{1},S_{2})}
=
{\displaystyle =}
+
3
2
n
R
T
0
(
V
0
V
2
)
2
/
3
[
exp
(
2
3
S
1
n
R
)
−
exp
(
2
3
S
2
n
R
)
]
{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}\,\left[\exp \left({\frac {2}{3}}{\frac {S_{1}}{n\,R}}\right)-\,\exp \left({\frac {2}{3}}{\frac {S_{2}}{n\,R}}\right)\right]}
(
V
,
S
:
V
2
S
2
→
V
2
S
1
)
,
d
N
=
0
{\displaystyle \qquad (V,S:V_{2}S_{2}\to V_{2}S_{1}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
W
S
1
,
N
(
V
1
,
V
2
)
{\displaystyle W_{S1,N}(V_{1},V_{2})}
=
{\displaystyle =}
+
3
2
n
R
T
0
[
(
V
0
V
1
)
2
/
3
−
(
V
0
V
2
)
2
/
3
]
exp
(
2
3
S
1
−
S
0
n
R
)
{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}-\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}\right]\,\exp \left({\frac {2}{3}}{\frac {S_{1}-S_{0}}{n\,R}}\right)}
(
V
,
S
:
V
2
S
1
→
V
1
S
1
)
,
d
N
=
0
{\displaystyle \qquad (V,S:V_{2}S_{1}\to V_{1}S_{1}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
0
{\displaystyle 0}
=
{\displaystyle =}
Q
V
1
,
N
(
S
2
,
S
1
)
+
W
S
2
,
N
(
V
2
,
V
1
)
{\displaystyle Q_{V1,N}(S_{2},S_{1})+W_{S2,N}(V_{2},V_{1})}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
{\displaystyle }
{\displaystyle }
+
Q
V
2
,
N
(
S
1
,
S
2
)
+
W
S
1
,
N
(
V
1
,
V
2
)
{\displaystyle +\,Q_{V2,N}(S_{1},S_{2})+W_{S1,N}(V_{1},V_{2})}
(
V
S
:
11
→
12
→
22
→
21
→
11
)
,
d
N
=
0
{\displaystyle \qquad (VS: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 =}
+
3
2
n
R
T
0
[
(
V
0
V
1
)
2
/
3
−
(
V
0
V
2
)
2
/
3
]
{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}-\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}\right]}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
{\displaystyle }
{\displaystyle }
×
[
exp
(
2
3
S
2
n
R
)
−
exp
(
2
3
S
1
n
R
)
]
{\displaystyle \times \left[\exp \left({\frac {2}{3}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{3}}{\frac {S_{1}}{n\,R}}\right)\right]}
(
V
S
:
11
→
12
→
22
→
21
→
11
)
,
d
N
=
0
{\displaystyle \qquad (VS: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 =}
−
3
2
n
R
T
0
[
(
V
0
V
1
)
2
/
3
−
(
V
0
V
2
)
2
/
3
]
{\displaystyle -\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}-\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}\right]}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
{\displaystyle }
{\displaystyle }
×
[
exp
(
2
3
S
2
n
R
)
−
exp
(
2
3
S
1
n
R
)
]
{\displaystyle \times \left[\exp \left({\frac {2}{3}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{3}}{\frac {S_{1}}{n\,R}}\right)\right]}
(
V
S
:
11
→
12
→
22
→
21
→
11
)
,
d
N
=
0
{\displaystyle \qquad (VS:11\to 12\to 22\to 21\to 11),\,dN=0\qquad }
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![{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}\,\left[\exp \left({\frac {2}{3}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{3}}{\frac {S_{1}}{n\,R}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bb39cd2fcbe5b3a7e14d109e66d6c73988a70c22)
![{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}-\,\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}\right]\,\exp \left({\frac {2}{3}}{\frac {S_{2}-S_{0}}{n\,R}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13c13929df76d6d0b68cc9872b0870e455fcae25)
![{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}\,\left[\exp \left({\frac {2}{3}}{\frac {S_{1}}{n\,R}}\right)-\,\exp \left({\frac {2}{3}}{\frac {S_{2}}{n\,R}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/478dcb5fcc89506f0c442de2fea8a9737bf00773)
![{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}-\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}\right]\,\exp \left({\frac {2}{3}}{\frac {S_{1}-S_{0}}{n\,R}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/661c95c1c4a6b7bc9f521166e56961cb72a6682e)
![{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}-\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a0e5f1df5b8a71ead7ae49db97e07b0ea808e33)
![{\displaystyle \times \left[\exp \left({\frac {2}{3}}{\frac {S_{2}}{n\,R}}\right)-\,\exp \left({\frac {2}{3}}{\frac {S_{1}}{n\,R}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37c2b975705ab7a8922b20568de80d8dc01e6a49)
![{\displaystyle -\,{\frac {3}{2}}\,n\,R\,T_{0}\,\left[\left({\frac {V_{0}}{V_{1}}}\right)^{2/3}-\,\left({\frac {V_{0}}{V_{2}}}\right)^{2/3}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d20226aaf81753b8d256231d7f7da07af82e8c2f)
