Please include sample calculations. Thank you. Question1 Using the attached ther
ID: 700927 • Letter: P
Question
Please include sample calculations. Thank you.
Question1 Using the attached thermodynamic data, make a chart of enthalpy increments for Fe, Cu, and Al203 over the interval 25°C to 2500°C and plot enthalpy as a function of temperature Cp=a+bT-cT-2 GIVEN: Heat Capacity Functions (J/mol Min. Valid Temp, °C 25 1084 25 760 911 1392 1537 25 2051 Max. Valid Temp., C 1084 2500 760 911 1392 1537 2700 2051 2500 22.64 31.38 12.73 48.59 24.28 28.21 40.90 106.61 114.11 6.28E-03 0 Cu 0 After fusion 3.17E-02 2.55E+05 8.29E-03 6.70E-03 1.67E-03 1.78E-02 2.85E+06 phase phase phase After fusion 0 A1203 0 After fusion GIVEN: Enthalpies of Phase Transformation Htri, J/mol 1365 670 840 13,770 12,977 107,580 ,°C Note 760 914 1391 1536 1084 2051 Fe Cu AI203 Fusion Fusion FusionExplanation / Answer
For Cu
Cp = a + bT - cT-2
Enthalpy change from 25 C to 1084 c
dH = Cp dT
Put the value of Cp and On Integrate the equation
H1 = 22.64 * (1084-25) +( 6.28*10^-3/2)*(10842 - 252) - (0)
= 23975.76 + 3687.71
= 27663.47 J/mol
Phase change at 1084 C
H2 = 12977 J/mol
Similarly Enthalpy change from 1084 c to 2500 c
H3 = 31.38 * (2500 - 1084) +( 0) - (0)
= 1184.96 J/mol
Total enthalpy = 27663.47 + 12977 + 1184.96
= 41825.43 J/mol
For Fe
Enthalpy change from 25 C to 760 c
H1 = 12.73 * (760-25) +(3.17*10^-2/2)*(7602 - 252) +(2.55*10^5)*(760-1 - 25-1)
= 9356.55 + 9145.053 - 9864.47
= 8637.133 J/mol
Phase change at 760 C
H2 = 1365 J/mol
Enthalpy change from 760 C to 911 c
H3 = 48.59 * (911 - 760)
= 7337.09 J/mol
Enthalpy change from 911 C to 914 c
H4 = 24.28 * (914-911) +(8.29*10^-3/2)*(9142 - 9112)
= 72.84 + 22.693
= 95.533 J/mol
Phase change at 914 C
H5 = 670 J/mol
Enthalpy change from 914 C to 1391 c
H6 = 24.28 * (1391 - 914) +(8.29*10^-3/2)*(13912 - 9142)
= 11581.56 + 4557.365
= 16138.925 J/mol
Phase change at 1391 C
H7 = 840 J/mol
Enthalpy change from 1391 C to 1392 c
H8 = 24.28 * (1392 - 1391) +(8.29*10^-3/2)*(13922 - 13912)
= 24.28 + 11.53
= 35.81 J/mol
Enthalpy change from 1392 C to 1536 C
H9 = 28.21 * (1536 - 1392 ) +(6.7*10^-3/2)*(15362 - 13922)
= 4062.24 + 1412.4672
= 5474.7072 J/mol
Phase change at 1536 C
H10 = 13770 J/mol
Enthalpy change from 1536 C to 1537 C
H11 = 28.21 * (1537 - 1536) +(6.7*10^-3/2)*(15372 - 15362)
= 28.21 + 10.29455
= 38.50455 J/mol
Enthalpy change from 1537 C to 2500 C
H12 = 40.90 * (2500 - 1537) +(1.67*10^-3/2)*(25002 - 15372)
= 39386.7 + 3246.171885
= 42632.871885 J/mol
Total enthalpy change of Fe from 25 to 2500 C
= 8637.133 + 1365 + 7337.09 + 95.533 + 670 + 16138.925 + 840 + 35.81 + 5474.7072 +13770 +38.50455 + 42632.871885
= 97035.575 J/mol
For Al2O3
Enthalpy change from 25 C to 2051 c
H1 = 106.61 * (2051-25) +(1.78*10^-2/2)*(20512 - 252) +(2.85*10^6)*(2051-1 - 25-1)
= 215991.86 + 37433.1864 - 112610.43
= 140814.6164 J/mol
Phase change at 2051 C
H2 = 107850 J/mol
Enthalpy change from 2051 C to 2500 c
H3 = 114.11 * (2500 - 2051)
= 51235.39 J/mol
Total enthalpy change = 140814.6164 + 107850 +51235.39
= 299900 J/mol