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Enthalpy of Mn in Molten Iron
A P P E N D I X
U
Enthalpy of Mn in Molten Iron To determine the enthalpy of Mn-bearing blast furnace iron, we treat the iron as molten FeMn alloy. It is not an ideal solution, so its enthalpy can’t be represented by HFe and HMn . We represent it by; H1500 C ; MJ=kg mol of Fe; and
FeðlÞ
H
1500 C MnðdissolvedÞ
8 < 5 H1500 C 1 ΔH : MnðlÞ
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
9 = ; ;
MJ=kg mol of Mn (U.1)
where ΔH
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
is the enthalpy
change for the Feð‘Þ 1 Mnð‘Þ-ðFe MnÞmolten alloy alloy formation reaction, 1500 C. Per kg of Mn in alloy, Eq. (U.1), becomes: H
They are also all based on 0.5 mass% Mn, 99.5 mass% Fe, FeMn alloy. We have to use this simplification because Feð‘Þ 1 Mnð‘Þ 1 Sið‘Þ 1 CðsÞ-molten alloy heats of reaction are not available. Witusiewicz’s enthalpy data are presented as a function of mol fraction Mn in FeMn alloy. So we start our calculations by determining mol fraction Mn in 0.5 mass% Mn, 99.5 mass%, FeMn alloy. We consider 100 kg of alloy. It contains 0.5 kg of Mn and 99.5 kg of Fe. The molecular mass of Mn and Fe are 54.94 and 55.85 kg/ kg mol so that; kg mol Mn 5
1500 C MnðdissolvedÞ
kg mol Fe 5
MWMn 9 8 ΔH 1500 C > >H 1500 C > > = < FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy MnðlÞ ; MJ=kg of Mn 5 1 > > MWMn MWMn > > ; :
99:5 kg Fe 5 1:78 55:85 kg Fe=kg mol of Fe
per 100 kg of alloy which are equivalent to;
(U.2)
XMn 5
U.1 CALCULATION OF ALLOY MOL FRACTIONS
XFe 5
This appendix’s calculations are based on Witusiewicz’s interpolated FeMn enthalpy of mixing data (Witusiewicz et al.,1 Fig. 1, Eq. 11).
0:5 kg Mn 5 0:0091 54:94 kg Mn=kg mol of Mn
0:0091 kg mol Mn 5 0:0051 ð0:0091 1 1:78Þ total kg mol
1:78 kg mol Fe 5 0:9949 ð0:0091 1 1:78Þ total kg mol
where XMn and XFe are the mol fractions of Mn and Fe in 0.5 mass% Mn, 99.5 mass% Fe alloy.
727
728
APPENDIX U: ENTHALPY OF MN IN MOLTEN IRON
U.2 CALCULATIONS: UNIT CONVERSIONS Witusiewicz’s interpolated enthalpy of mixing data is for 1427 C. We make the assumption that they are nearly the same as our required 1500 C enthalpy of mixing, that is we assume that: ΔH
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
Witusiewicz’s1 ΔH
1427 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
5 ΔH
divide the above value by the atomic mass of manganese, that is: ΔH
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
MWMn 5
2 4 MJ=kg mol of Mn in the molten alloy 54:94 kg=kg mol of Mn
5 0:07 MJ=kg of Mn in the molten alloy
1427 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
U.5 H
=MWMn 1500 C MnðdissolvedÞ
interpolated value for 0.0091 mol
fraction Mn (i.e., 0.5 mass% Mn) is 20 J/g mol of alloy or 20 kJ/kg mol of alloy or 0.02 MJ/kg mol of alloy.
U.3 ENTHALPY PER kg mol OF MANGANESE
The term we use in enthalpy equation of Chapter 36, Bottom-Segment CalculationsReduction of MnO, is H 1500 C =MWMn :
MnðdissolvedÞ
It is calculated by the equation; H
1500 C MnðdissolvedÞ
MWMn
5
8H > < 1500 C MnðlÞ
> : MWMn
ΔH 1
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
MWMn
9 > = ; > ;
This section calculates; ΔH
MJ=kg of Mn 1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
per kg mol of Mn in molten 0.5 mass% Mn, 99.5 mass% Fe molten FeMn alloy. As shown in Section U.1, 1 kg mol of this alloy contains 0.0051 kg mol of Mn per kg mol of molten alloy, so 0.02 MJ/kg mol of molten alloy is equivalent to; 2 0:02 MJ=kg mol of molten alloy 0:0051 kg mol of Mn per kg mol of molten alloy
or 2 4MJ/kg mol of Mn in the molten alloy. This value is used in Chapter 36, BottomSegment Calculations-Reduction of MnO, and throughout the book.
where from Appendix J; H1500 C MnðlÞ
MWMn
5 1:343 MJ=kg of Mn
and from Section U.4; ΔH
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
MWMn
5 0:07 MJ=kg of dissolved Mn
giving: H
1500 C MnðdissolvedÞ
MWMn
5
8 H 1500 C > > < MnðlÞ
> MWMn > :
ΔH 1
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
MWMn
9 > > = > > ;
5 1:343 1 ð0:07Þ 5 1:27 MJ=kg of dissolved Mn:
U.4 PER kg mol OF MANGANESE Chapter 36, Bottom-Segment CalculationsReduction of MnO, uses the enthalpy of alloy formation per kg of manganese. To get this, we
Reference 1. Witusiewicz VT, Sommer F, Mittemeijer EJ. Enthalpy of formation and heat capacity of FeMn alloys. Metall Mater Trans B 2003;34B:20923 (Equation 11, page 213).
U
Enthalpy of Mn in Molten Iron To determine the enthalpy of Mn-bearing blast furnace iron, we treat the iron as molten FeMn alloy. It is not an ideal solution, so its enthalpy can’t be represented by HFe and HMn . We represent it by; H1500 C ; MJ=kg mol of Fe; and
FeðlÞ
H
1500 C MnðdissolvedÞ
8 < 5 H1500 C 1 ΔH : MnðlÞ
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
9 = ; ;
MJ=kg mol of Mn (U.1)
where ΔH
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
is the enthalpy
change for the Feð‘Þ 1 Mnð‘Þ-ðFe MnÞmolten alloy alloy formation reaction, 1500 C. Per kg of Mn in alloy, Eq. (U.1), becomes: H
They are also all based on 0.5 mass% Mn, 99.5 mass% Fe, FeMn alloy. We have to use this simplification because Feð‘Þ 1 Mnð‘Þ 1 Sið‘Þ 1 CðsÞ-molten alloy heats of reaction are not available. Witusiewicz’s enthalpy data are presented as a function of mol fraction Mn in FeMn alloy. So we start our calculations by determining mol fraction Mn in 0.5 mass% Mn, 99.5 mass%, FeMn alloy. We consider 100 kg of alloy. It contains 0.5 kg of Mn and 99.5 kg of Fe. The molecular mass of Mn and Fe are 54.94 and 55.85 kg/ kg mol so that; kg mol Mn 5
1500 C MnðdissolvedÞ
kg mol Fe 5
MWMn 9 8 ΔH 1500 C > >H 1500 C > > = < FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy MnðlÞ ; MJ=kg of Mn 5 1 > > MWMn MWMn > > ; :
99:5 kg Fe 5 1:78 55:85 kg Fe=kg mol of Fe
per 100 kg of alloy which are equivalent to;
(U.2)
XMn 5
U.1 CALCULATION OF ALLOY MOL FRACTIONS
XFe 5
This appendix’s calculations are based on Witusiewicz’s interpolated FeMn enthalpy of mixing data (Witusiewicz et al.,1 Fig. 1, Eq. 11).
0:5 kg Mn 5 0:0091 54:94 kg Mn=kg mol of Mn
0:0091 kg mol Mn 5 0:0051 ð0:0091 1 1:78Þ total kg mol
1:78 kg mol Fe 5 0:9949 ð0:0091 1 1:78Þ total kg mol
where XMn and XFe are the mol fractions of Mn and Fe in 0.5 mass% Mn, 99.5 mass% Fe alloy.
727
728
APPENDIX U: ENTHALPY OF MN IN MOLTEN IRON
U.2 CALCULATIONS: UNIT CONVERSIONS Witusiewicz’s interpolated enthalpy of mixing data is for 1427 C. We make the assumption that they are nearly the same as our required 1500 C enthalpy of mixing, that is we assume that: ΔH
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
Witusiewicz’s1 ΔH
1427 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
5 ΔH
divide the above value by the atomic mass of manganese, that is: ΔH
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
MWMn 5
2 4 MJ=kg mol of Mn in the molten alloy 54:94 kg=kg mol of Mn
5 0:07 MJ=kg of Mn in the molten alloy
1427 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
U.5 H
=MWMn 1500 C MnðdissolvedÞ
interpolated value for 0.0091 mol
fraction Mn (i.e., 0.5 mass% Mn) is 20 J/g mol of alloy or 20 kJ/kg mol of alloy or 0.02 MJ/kg mol of alloy.
U.3 ENTHALPY PER kg mol OF MANGANESE
The term we use in enthalpy equation of Chapter 36, Bottom-Segment CalculationsReduction of MnO, is H 1500 C =MWMn :
MnðdissolvedÞ
It is calculated by the equation; H
1500 C MnðdissolvedÞ
MWMn
5
8H > < 1500 C MnðlÞ
> : MWMn
ΔH 1
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
MWMn
9 > = ; > ;
This section calculates; ΔH
MJ=kg of Mn 1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
per kg mol of Mn in molten 0.5 mass% Mn, 99.5 mass% Fe molten FeMn alloy. As shown in Section U.1, 1 kg mol of this alloy contains 0.0051 kg mol of Mn per kg mol of molten alloy, so 0.02 MJ/kg mol of molten alloy is equivalent to; 2 0:02 MJ=kg mol of molten alloy 0:0051 kg mol of Mn per kg mol of molten alloy
or 2 4MJ/kg mol of Mn in the molten alloy. This value is used in Chapter 36, BottomSegment Calculations-Reduction of MnO, and throughout the book.
where from Appendix J; H1500 C MnðlÞ
MWMn
5 1:343 MJ=kg of Mn
and from Section U.4; ΔH
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
MWMn
5 0:07 MJ=kg of dissolved Mn
giving: H
1500 C MnðdissolvedÞ
MWMn
5
8 H 1500 C > > < MnðlÞ
> MWMn > :
ΔH 1
1500 C FeðlÞ1MnðlÞ-ðFe2MnÞmolten alloy
MWMn
9 > > = > > ;
5 1:343 1 ð0:07Þ 5 1:27 MJ=kg of dissolved Mn:
U.4 PER kg mol OF MANGANESE Chapter 36, Bottom-Segment CalculationsReduction of MnO, uses the enthalpy of alloy formation per kg of manganese. To get this, we
Reference 1. Witusiewicz VT, Sommer F, Mittemeijer EJ. Enthalpy of formation and heat capacity of FeMn alloys. Metall Mater Trans B 2003;34B:20923 (Equation 11, page 213).