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PCRT.I.G.03
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PCRT.I.G
03 (N,V,T)-Koordinatensystem
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{\displaystyle \qquad \qquad }
d
Q
N
{\displaystyle dQ_{N}}
=
{\displaystyle =}
d
Q
V
,
N
+
d
Q
T
,
N
{\displaystyle dQ_{V,N}+dQ_{T,N}}
d
Q
N
(
V
,
T
)
{\displaystyle \qquad dQ_{N}(V,T)\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
(
T
)
{\displaystyle \qquad dU_{V,N}(T)\qquad }
{\displaystyle \qquad \qquad }
d
Q
T
,
N
{\displaystyle dQ_{T,N}}
=
{\displaystyle =}
d
U
T
,
N
−
d
F
T
,
N
{\displaystyle dU_{T,N}-dF_{T,N}}
d
U
T
,
N
(
V
)
,
d
F
T
,
N
(
V
)
{\displaystyle \qquad dU_{T,N}(V),\,dF_{T,N}(V)\qquad }
{\displaystyle \qquad \qquad }
d
W
N
{\displaystyle dW_{N}}
=
{\displaystyle =}
d
W
V
,
N
+
d
W
T
,
N
{\displaystyle dW_{V,N}+dW_{T,N}}
d
W
N
(
V
,
T
)
,
d
W
V
,
N
(
T
)
,
d
W
T
,
N
(
V
)
{\displaystyle \qquad dW_{N}(V,T),\,dW_{V,N}(T),\,dW_{T,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
T
,
N
{\displaystyle dW_{T,N}}
=
{\displaystyle =}
d
F
T
,
N
{\displaystyle dF_{T,N}}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
d
U
N
{\displaystyle dU_{N}}
=
{\displaystyle =}
d
U
V
,
N
+
d
U
T
,
N
{\displaystyle dU_{V,N}+dU_{T,N}}
d
U
N
(
V
,
T
)
{\displaystyle \qquad dU_{N}(V,T)\qquad }
{\displaystyle \qquad }
F
{\displaystyle F}
=
{\displaystyle =}
−
n
R
T
−
3
2
n
R
T
ln
(
T
T
0
)
−
n
R
T
ln
(
V
V
0
)
{\displaystyle -\,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)}
F
(
N
,
V
,
T
)
{\displaystyle \qquad F(N,V,T)\qquad }
{\displaystyle \qquad \qquad }
U
{\displaystyle U}
=
{\displaystyle =}
+
3
2
n
R
T
{\displaystyle +\,{\frac {3}{2}}\,n\,R\,T}
U
(
N
,
V
,
T
)
{\displaystyle \qquad U(N,V,T)\qquad }
{\displaystyle \qquad \qquad }
Q
V
1
,
N
(
T
2
,
T
1
)
{\displaystyle Q_{V1,N}(T_{2},T_{1})}
=
{\displaystyle =}
3
2
n
R
(
T
2
−
T
1
)
{\displaystyle {\frac {3}{2}}\,n\,R\,(T_{2}-T_{1})}
(
V
,
T
:
V
1
T
1
→
V
1
T
2
)
,
d
N
=
0
{\displaystyle \qquad (V,T:V_{1}T_{1}\to V_{1}T_{2}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
Q
T
2
,
N
(
V
2
,
V
1
)
{\displaystyle Q_{T2,N}(V_{2},V_{1})}
=
{\displaystyle =}
+
n
R
T
2
[
ln
V
2
V
0
−
ln
V
1
V
0
]
{\displaystyle +\,n\,R\,T_{2}\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\right]}
(
V
,
T
:
V
1
T
2
→
V
2
T
2
)
,
d
N
=
0
{\displaystyle \qquad (V,T:V_{1}T_{2}\to V_{2}T_{2}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
W
T
2
,
N
(
V
2
,
V
1
)
{\displaystyle W_{T2,N}(V_{2},V_{1})}
=
{\displaystyle =}
−
n
R
T
2
[
ln
V
2
V
0
−
ln
V
1
V
0
]
{\displaystyle -\,n\,R\,T_{2}\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\right]}
(
V
,
T
:
V
1
T
2
→
V
2
T
2
)
,
d
N
=
0
{\displaystyle \qquad (V,T:V_{1}T_{2}\to V_{2}T_{2}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
Q
V
2
,
N
(
T
1
,
T
2
)
{\displaystyle Q_{V2,N}(T_{1},T_{2})}
=
{\displaystyle =}
3
2
n
R
(
T
1
−
T
2
)
{\displaystyle {\frac {3}{2}}\,n\,R\,(T_{1}-T_{2})}
(
V
,
T
:
V
2
T
2
→
V
2
T
1
)
,
d
N
=
0
{\displaystyle \qquad (V,T:V_{2}T_{2}\to V_{2}T_{1}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
Q
T
1
,
N
(
V
1
,
V
2
)
{\displaystyle Q_{T1,N}(V_{1},V_{2})}
=
{\displaystyle =}
+
n
R
T
1
[
ln
V
1
V
0
−
ln
V
2
V
0
]
{\displaystyle +\,n\,R\,T_{1}\,\left[\ln {\frac {V_{1}}{V_{0}}}-\ln {\frac {V_{2}}{V_{0}}}\right]}
(
V
,
T
:
V
2
T
1
→
V
1
T
1
)
,
d
N
=
0
{\displaystyle \qquad (V,T:V_{2}T_{1}\to V_{1}T_{1}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
W
T
1
,
N
(
V
1
,
V
2
)
{\displaystyle W_{T1,N}(V_{1},V_{2})}
=
{\displaystyle =}
−
n
R
T
1
[
ln
V
1
V
0
−
ln
V
2
V
0
]
{\displaystyle -\,n\,R\,T_{1}\,\left[\ln {\frac {V_{1}}{V_{0}}}-\ln {\frac {V_{2}}{V_{0}}}\right]}
(
V
,
T
:
V
2
T
1
→
V
1
T
1
)
,
d
N
=
0
{\displaystyle \qquad (V,T:V_{2}T_{1}\to V_{1}T_{1}),\,dN=0\qquad }
{\displaystyle \qquad \qquad }
0
{\displaystyle 0}
=
{\displaystyle =}
Q
V
1
,
N
(
T
2
,
T
1
)
+
Q
T
2
,
N
(
V
2
,
V
1
)
+
W
T
2
,
N
(
V
2
,
V
1
)
{\displaystyle Q_{V1,N}(T_{2},T_{1})+Q_{T2,N}(V_{2},V_{1})+W_{T2,N}(V_{2},V_{1})}
{\displaystyle \qquad \qquad }
{\displaystyle \qquad \qquad }
{\displaystyle }
{\displaystyle }
+
Q
V
2
,
N
(
T
1
,
T
2
)
+
W
T
1
,
N
(
V
1
,
V
2
)
+
W
T
1
,
N
(
V
1
,
V
2
)
{\displaystyle +\,Q_{V2,N}(T_{1},T_{2})+W_{T1,N}(V_{1},V_{2})+W_{T1,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 =}
+
n
R
(
T
2
−
T
1
)
[
ln
V
2
V
0
−
ln
V
1
V
0
]
{\displaystyle +\,n\,R\,(T_{2}-T_{1})\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\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 =}
−
n
R
(
T
2
−
T
1
)
[
ln
V
2
V
0
−
ln
V
1
V
0
]
{\displaystyle -\,n\,R\,(T_{2}-T_{1})\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\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 +\,n\,R\,T_{2}\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c6b40688b05da9771ca63158d3cafa454bdbb9a)
![{\displaystyle -\,n\,R\,T_{2}\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/71ef4c8e53fe5b67b211171fcb54e9e6a3f4e490)
![{\displaystyle +\,n\,R\,T_{1}\,\left[\ln {\frac {V_{1}}{V_{0}}}-\ln {\frac {V_{2}}{V_{0}}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b1abc804fe59aff5af42479fb52cfaf956c0ed76)
![{\displaystyle -\,n\,R\,T_{1}\,\left[\ln {\frac {V_{1}}{V_{0}}}-\ln {\frac {V_{2}}{V_{0}}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/801ea45a528d72f55fe2f8d397f3574fdb05b16c)
![{\displaystyle +\,n\,R\,(T_{2}-T_{1})\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cc395000949874f1bb03ddf9d885b164358c74f9)
![{\displaystyle -\,n\,R\,(T_{2}-T_{1})\,\left[\ln {\frac {V_{2}}{V_{0}}}-\ln {\frac {V_{1}}{V_{0}}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/80a49b168a09ff1a91415dc459d4d634153e9e20)
