Final Exam

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a) Write the Gibbs equation for free energy and specify the terms in the equation and their respective units in the SI system.

G = U + PV – TSb= H – TS

Where G = Gibbs free energy(Joule)H =Enthalpy(Joule)
U = Internal energy(Joule)
P = Pressure(Pa)
V = Volume(m3)
T = Temperature (K)
S = Entropy(Joule/K)

b) Write the Gibbs phase rule and explain the meaning of the terms in the equation.

F = VAR – REL (where VAR= P(C+1), REL = (P-1)(C+2))
F = P(C+1) – (P-1)(C+2)
F = C – P + 2

Where F = The number of degrees of freedom
C = The number of components
P = The number of phases

c)For most applications for solid alloys it is convenient to use the reduced phase rule, explain what it is. Reduced phase rule ; F = C – P + 1
F(degree of freedom) is the number of the intensive variables which can independently change with maintaining the equilibrium, such as T, P, XA, XB. For condensed phases the thermodynamic properties are relatively insensitive to pressure and it is usual to assume that the pressure is fixed at 1 atm. Therefore, if the pressure is fixed, degree of freedom decreases by one.

d) Draw a schematic binary peritectic phase diagram, mark the phase fields. e) Draw schematic Gibbs energy curves for the system in pard d) at the peritectic temperature.

a) Use Thermocalc to tabulate the Gibbs energy and equilibrium constant K as a function of temperature from 300K to 1700K for the oxidation of titanium. Include a log file in your answer that shows your input responses. O U T P U T F R O M T H E R M O - C A L C

2012.12. 5 21.15. 8

Column 6: K EXP(-G/R/T )
Reaction: O2+TI=O2TI1
O2 stable as GAS
TI stable as TI_S
O2TI1 stable as RUTILE

****************************************************************************** T Delta-Cp Delta-H Delta-S Delta-G K (K) (Joule/K) (Joule) (Joule/K) (Joule) ****************************************************************************** 300.00 6.72890E-01 -9.43999E+05 -1.85243E+02 -8.88426E+05 4.83937+154 400.00 4.52905E+00 -9.43704E+05 -1.84421E+02 -8.69936E+05 3.97243+113 500.00 5.83556E+00 -9.43174E+05 -1.83244E+02 -8.51552E+05 9.09460E+88 600.00 6.24376E+00 -9.42566E+05 -1.82136E+02 -8.33284E+05 3.48331E+72 700.00 6.31946E+00 -9.41936E+05 -1.81166E+02 -8.15120E+05 6.66000E+60 800.00 6.29900E+00 -9.41305E+05 -1.80323E+02 -7.97047E+05 1.09772E+52 900.00 6.29974E+00 -9.40676E+05 -1.79582E+02 -7.79052E+05 1.63632E+45 1000.00 6.27895E+00 -9.40047E+05 -1.78919E+02 -7.61128E+05 5.70462E+39 1100.00 6.25722E+00 -9.39420E+05 -1.78322E+02 -7.43266E+05 1.96730E+35 1155. ---- TI becomes TI_S2 ,delta-H = 4170.00

1200.00 1.14930E+01 -9.42734E+05 -1.81192E+02 -7.25303E+05 3.72256E+31 1300.00 1.18354E+01 -9.41566E+05 -1.80257E+02 -7.07231E+05 2.60729E+28 1400.00 1.19942E+01 -9.40373E+05 -1.79373E+02 -6.89250E+05 5.19513E+25 1500.00 1.19912E+01 -9.39172E+05 -1.78545E+02 -6.71355E+05 2.38817E+23 1600.00 1.18415E+01 -9.37980E+05 -1.77775E+02 -6.53539E+05 2.16438E+21 1700.00 1.15559E+01 -9.36809E+05 -1.77065E+02 -6.35798E+05 3.42924E+19

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