![Page 1: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/1.jpg)
∆G
z.B. Forsterit - Fayalit
0.1
0
10.2 0.3 0.4 0.90.60.5 0.80.7
XB
???
???
€
Δ aGFoT ,P
€
Δ aGFaT ,P
MgSi0.5O2 FeSi0.5O2
€
xA ⋅ΔaGA + xB ⋅ΔaGB
Ideale Lösungen
![Page 2: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/2.jpg)
BA
B
B
B
B
B
B
B
B
B
B
A
A A
A
A A
A
A
A
A
A
A
A
A
A
A
A
B
B
BB
B
B
BB
B
B
B
AAA
A
A
AA
A
A
A
A
A
A
A
A
A
A
A
NA
VA
NB
VB
N=NB+NA
V
∆Smix = ?∆Hmix = ?
∆Gmix = ∆Hmix-T· ∆Smix
![Page 3: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/3.jpg)
Der erste Hauptsatz der Thermodynamik(die folgende Formulierung setzt den zweiten Hauptsatz voraus)
dU = Q + A
dU = T·dS - P·dV
Definitionen
H = U + PVG = U + PV - TSG = H -TS
![Page 4: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/4.jpg)
Wie wir uns ein ideales Gas vorstellen
v
Partikel (Masse = M, Grösse = 0), die sich mit der Geschwindigkeit v in alle Richtungen bewegen.
Temperatur: ist von der Geschwindigkeit abhängigDruck: Entsteht wegen Impulserhaltung bei elastischem Stoss auf die Wände
Daraus folgt ... n·R·T = P·V
R = Gaskonstante = k·N = 8.3144 (J/mol K)N = Avogadro-Konstante = 6.022·1023 (1/mol)k = Boltzmann-Konstante = 1.38 ·10-23 (J/K)
![Page 5: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/5.jpg)
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B
B
B
B
B
B
B
B
B
B
A
A A
A
A A
A
A
A
A
A
A
A
A
A
A
A
B
B
BB
B
B
BB
B
B
B
AAA
A
A
AA
A
A
A
A
A
A
A
A
A
A
A
NA
VA
NB
VB
N=NB+NA
V
∆Smix = ?∆Hmix = ?
∆Gmix = ∆Hmix-T· ∆Smix
![Page 6: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/6.jpg)
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B
B
B
B
B
B
B
B
B
B
A
A A
A
A A
A
A
A
A
A
A
A
A
A
A
A
A
AA
A
A
AA
AA
A
A
A
A
A
A
A
A
A
B
B
B
B
B
B
BB
B
B
B
B
B
BB
B
B
BB
B
B
B
AAA
A
A
AA
A
A
A
A
A
A
A
A
A
A
A
1. isotherme Expansion
2. reversibles Mischen
NA
VA = V·(NA/N)
NB
VB = V·(NB/N)
NA
V
NB
V
NB+NA
V
NA+NB=N
![Page 7: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/7.jpg)
Irreversibel Reversibel
T=constdU=0Q≠0A≠0
(∆T=0)dU=0Q=0A=0
dU=TdS-PdV=0dS=(P/T)dV
€
ΔS = dS =1
2
∫P
TV0
V
∫ dV =ΔA
T
(ideales GasP
T=R
V)
ΔS =R
VdV
V0
V
∫
ΔS = R ⋅ lnV
V0
⎛
⎝ ⎜
⎞
⎠ ⎟
ΔS = N ⋅k ⋅ lnV
V0
⎛
⎝ ⎜
⎞
⎠ ⎟
V0
V
V0
V
isotherme Expansion
∆G = ∆U + ∆(PV) - ∆(TS)
ideales Gas: PV=RT, ∆U=0, ∆T=0
∆G = -T·∆S
(Versuch von Gay-Lussac)
![Page 8: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/8.jpg)
BA
B
B
B
B
B
B
B
B
B
B
A
A A
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A A
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A
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A
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B
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B
B
B
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B
B
B
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B
B
BB
B
B
B
AAA
A
A
AA
A
A
A
A
A
A
A
A
A
A
A
1. isotherme Expansion: ∆S=N·k·ln(V/V0)
2. reversibles Mischen
NA
VA = V·(NA/N)
NB
VB = V·(NB/N)
NA
V
NB
V
NB+NA
V
NA+NB=N
![Page 9: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/9.jpg)
A
AA
A
A
AA
AA
A
A
A
A
A
A
A
A
A
B
B
B
B
B
B
BB
B
B
B
B
B
BB
B
B
BB
B
B
B
AAA
A
A
AA
A
A
A
A
A
A
A
A
A
A
A
NA
V
NB
V
NB+NA
V
∆S = ?
2. reversibles Mischen
![Page 10: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/10.jpg)
B
BB
B
B BB
BB
B B
BB
0
AA
A
A
A
A
A AA
A
A A
NA
VNB
V
Reversibles Mischen
P = pA P = pB
![Page 11: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/11.jpg)
B
BB
B
B BB
BB
B B
BB
1
AA
A
A
A
A
A AA
A
A A
Reversibles Mischen
![Page 12: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/12.jpg)
B
BB
B
B BB
BB
B B
BB
2
AA
A
A
A
A
A AA
A
A A
Reversibles Mischen
P=pA P=pA
![Page 13: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/13.jpg)
B
BB
B
B BB
BB
B B
BB
3
AA
A
A
A
A
A AA
A
A A
Reversibles Mischen
![Page 14: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/14.jpg)
B
BB
B
B BB
BB
B B
BB
4
AA
A
A
A
A
A AA
A
A A
Reversibles Mischen
![Page 15: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/15.jpg)
B
BB
B
B BB
BB
B B
BB
5
AA
A
A
A
A
A AA
A
A A
Reversibles Mischen
![Page 16: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/16.jpg)
B
BB
B
B BB
BB
B B
BB
6
AA
A
A
A
A
A AA
A
A A
Reversibles Mischen
![Page 17: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/17.jpg)
B
BB
B
B BB
BB
B B
BB
7
AA
A
A
A
A
A AA
A
A A
Reversibles Mischen
![Page 18: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/18.jpg)
B
BB
B
B BB
BB
B B
BB
8
AA
A
A
A
A
A AA
A
A A
NA + NB
V
Reversibles Mischen
P = pA+pB
![Page 19: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/19.jpg)
B
BB
B
B BB
BB
B B
BB
9
AA
A
A
A
A
A AA
A
A A
NA + NB
V
(∆T=0)Q=0A=0dU=0
Reversibles Mischen
∆S = 0
![Page 20: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/20.jpg)
A
AA
A
A
AA
AA
A
A
A
A
A
A
A
A
A
B
B
B
B
B
B
BB
B
B
B
B
B
BB
B
B
BB
B
B
B
AAA
A
A
AA
A
A
A
A
A
A
A
A
A
A
A
NA
V
NB
V
NB+NA
V
∆S = 0
![Page 21: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/21.jpg)
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B
B
B
B
B
B
B
B
B
B
A
A A
A
A A
A
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A
A
A
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A
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A
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A
AA
A
A
AA
AA
A
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A
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A
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B
B
B
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B
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B
B
BB
B
B
B
AAA
A
A
AA
A
A
A
A
A
A
A
A
A
A
A
2. reversibles Mischen ∆S=0
NA
VA = V·(NA/N)
NB
VB = V·(NB/N)
NA
V
NB
V
NB+NA
V
NA+NB=N
1. isotherme Expansion: ∆S=N·k·ln(V/V0)
![Page 22: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/22.jpg)
BA
B
B
B
B
B
B
B
B
B
B
A
A A
A
A A
A
A
A
A
A
A
A
A
A
A
A
B
B
BB
B
B
BB
B
B
B
AAA
A
A
AA
A
A
A
A
A
A
A
A
A
A
A
NA
VA
NB
VB
N=NB+NA
V
∆Gmix = ∆Hmix-T· ∆Smix
€
ΔSmix = N ⋅k ⋅ lnV
V0
⎛
⎝ ⎜
⎞
⎠ ⎟
ΔHmix = 0
![Page 23: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/23.jpg)
![Page 24: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/24.jpg)
isotherme Expansion
∆S = k· (NA·ln(N) - NA·ln(NA) + NB·ln(N) - NB·ln(NB))
€
ΔS = NA ⋅k ⋅lnV
V ⋅NAN
+ NB ⋅k ⋅lnV
V ⋅NBN
∆S = k· (N·ln(N) - NA·ln(NA) - NB·ln(NB))
∆S = k· ( N·ln(N) - N·xA ·ln(N·xA) - N·xB ·ln(N·xB) )
xA = NA/N NA = N·xA xA + xB = 1xB = NB/N NB = N·xB
∆S = k· ( N·ln(N) -N·xA ·ln(N) -N·xA ·ln(xA) -N·xB ·ln(N) - N·xB ·ln(xB) )
∆S = k·N ·( ln(N)·(1-xA-xB) -xA ·ln(xA) -xB ·ln(xB) )
∆S = -R ·( xA ·ln(xA) + xB ·ln(xB) )
∆S = -R ·∑( xi ·ln(xi) )
A
A
![Page 25: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/25.jpg)
BA
B
B
B
B
B
B
B
B
B
B
A
A A
A
A A
A
A
A
A
A
A
A
A
A
A
A
B
B
BB
B
B
BB
B
B
B
AAA
A
A
AA
A
A
A
A
A
A
A
A
A
A
A
NA
VA
NB
VB
NB+NA
V
∆S = -R ·( xA ·ln(xA) + xB ·ln(xB) )
![Page 26: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/26.jpg)
![Page 27: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/27.jpg)
isotherme Expansion
∆S = k· (NA·ln(N) - NA·ln(NA) + NB·ln(N) - NB·ln(NB))
€
ΔS = NA ⋅k ⋅lnV
V ⋅NAN
+ NB ⋅k ⋅lnV
V ⋅NBN
∆S = k· (N·ln(N) - NA·ln(NA) - NB·ln(NB))
xA = NA/N NA = N·xA xA + xB = 1
∆S = k· ( N·ln(N) - N·xA ·ln(N·xA) - N·xB ·ln(N·xB) )
xB = NB/N NB = N·xB
∆S = k· ( N·ln(N) -N·xA ·ln(N) -N·xA ·ln(xA) -N·xB ·ln(N) - N·xB ·ln(xB) )
∆S = k·N ·( ln(N)·(1-xA-xB) -xA ·ln(xA) -xB ·ln(xB) )
∆S = -R ·( xA ·ln(xA) + xB ·ln(xB) )
∆S = -R ·∑( xi ·ln(xi) )
A
A
Statistische Mechanik
![Page 28: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/28.jpg)
∆S = k· (N·ln(N) - NA·ln(NA) - NB·ln(NB)) Statistische Mechanik
Stirling'sche Formel:
€
ln n!( ) ≈ n ⋅ln n( ) +1
2⋅ln n( ) − n + ln 2Π
n=1023 ≈ 50 ≈ 25 1023 ≈ 0.9
€
ln n!( ) ≈ n ⋅ln n( ) − n
n ⋅ln n( ) ≈ ln n!( ) + n
∆S = k· (N·ln(N) - NA·ln(NA) - NB·ln(NB))
€
ΔS = k ⋅ ln N!( ) + N − ln(NA!) −NA − ln(NB!) −NB( )
ΔS = k ⋅ ln N!( ) − ln(NA!) − ln(NB!)( )
ΔS = k ⋅lnN!
NA!⋅NB!= k ⋅ln
N
NA
⎛
⎝ ⎜
⎞
⎠ ⎟
![Page 29: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/29.jpg)
€
ΔS = k ⋅lnN!
NA!⋅NB!
A
B
NA+NB=N
€
N!
NA!⋅NB!= Anzahl Möglichkeiten NA Atome A und NB Atome B auf N Gitterplätze zu verteilen.= Anzahl Zustände des Systems welche alle die gleiche Energie haben.= (wird etwa "thermodynamische Wahrscheinlichkeit" genannt)= w (in der statistischen Mechanik)
S' = k·ln(w)
Getrennte A und B: w = 1 S' = 0(Mischung - getrennt): ∆S = k·ln(w)
![Page 30: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/30.jpg)
isotherme Expansion
∆S = k· (NA·ln(N) - NA·ln(NA) + NB·ln(N) - NB·ln(NB))
€
ΔS = NA ⋅k ⋅lnV
V ⋅NAN
+ NB ⋅k ⋅lnV
V ⋅NBN
∆S = k· (N·ln(N) - NA·ln(NA) - NB·ln(NB))
xA = NA/N NA = N·xA xA + xB = 1
∆S = k· ( N·ln(N) - N·xA ·ln(N·xA) - N·xB ·ln(N·xB) )
xB = NB/N NB = N·xB
∆S = k· ( N·ln(N) -N·xA ·ln(N) -N·xA ·ln(xA) -N·xB ·ln(N) - N·xB ·ln(xB) )
∆S = k·N ·( ln(N)·(1-xA-xB) -xA ·ln(xA) -xB ·ln(xB) )
∆S = -R·( xA ·ln(xA) + xB ·ln(xB) )
∆S = -R·∑( xi ·ln(xi) )
A
A
∆S = k·ln(w)
![Page 31: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/31.jpg)
∆G
z.B. Forsterit - Fayalit
0.1
0
10.2 0.3 0.4 0.90.60.5 0.80.7
XB
??????
€
Δ aGFoT ,P
€
Δ aGFaT ,P
∆S = -R·( xA ·ln(xA) + xB ·ln(xB) )∆Gmix = -T·∆S∆Gmix = R·T·( xA ·ln(xA) + xB ·ln(xB) )
MgSi0.5O2 FeSi0.5O2
€
xA ⋅ΔaGA + xB ⋅ΔaGBA B
![Page 32: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/32.jpg)
∆G
z.B. Forsterit - Fayalit
MgSi0.5O2 FeSi0.5O2
0.1
0
10.2 0.3 0.4 0.90.60.5 0.80.7
XB
€
Δ aGFoT ,P
€
Δ aGFaT ,P
∆Gmix = R·T·( xA ·ln(xA) + xB ·ln(xB) )
xB xA
€
xA ⋅ΔaGA + xB ⋅ΔaGBA B
![Page 33: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/33.jpg)
∆G
z.B. Forsterit - Fayalit
MgSi0.5O2 FeSi0.5O2
0.1
0
10.2 0.3 0.4 0.90.60.5 0.80.7
XB
€
Δ aGFoT ,P
€
Δ aGFaT ,P
∆Gmix = R·T·( xA ·ln(xA) + xB ·ln(xB) )
xB xA
€
xA ⋅ΔaGA + xB ⋅ΔaGBA B
∆Gtot=xA·∆aGA+ xB· ∆aGB + R·T·( xA ·ln(xA) + xB ·ln(xB) )
![Page 34: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/34.jpg)
∆G
z.B. Forsterit - Fayalit
MgSi0.5O2 FeSi0.5O2
0.1
0
10.2 0.3 0.4 0.90.60.5 0.80.7
XB
€
Δ aGFoT ,P
€
Δ aGFaT ,P
∆Gmix = R·T·( xA ·ln(xA) + xB ·ln(xB) )
xB xA
€
xA ⋅ΔaGA + xB ⋅ΔaGB
R·T·ln(xB)
R·T·ln(xA)
B
A
= 0B
0A=
∆Gtot=xA·A+ xB·B
A B
![Page 35: G z.B. Forsterit - Fayalit 0.1 0 10.20.30.40.90.60.50.80.7 XBXB ??? MgSi 0.5 O 2 FeSi 0.5 O 2 Ideale Lösungen](https://reader035.vdokument.com/reader035/viewer/2022070310/55204d7349795902118c843c/html5/thumbnails/35.jpg)