1.The following questions should be answered with rigor. (a)Is it correct to say that the Gibbs energy of a system always decrease as it undergoes change?Why Present a statement consistent with thermodynamics. (b)Is it correct to say that the activity of a component must be the same in two mutually equilibrated phases?Why?Formulate an acceptable statement. (c)Can the entropy of an adiabatic system decrease?If so,indicate how you would observe(measure)the entropy change. (d)Can Cp be less than Cv for a stable system?Support your answer? (e)Is it necessary to have an atomistic model to apply thermodynamic arguments? 2.Consider a crystalline solid of N atoms with coordination number Z and cohesive energy Ec. (a)Following a simplified model of the solid that takes into account only nearest-neighbor interactions,write down an expression for the formation energy of a vacancy,EDV.Do the same for a divacancy,EV.Remember to conserve numbers of atoms. (b)Next write down an expression for the configurational or mixing entropy of a system of nV vacancies in the solid.Do the same for a system of nDV divacancies.Remember to count all possible arrangements of the system.Assume that nV and nDV are much less than N. (c)Formulate expressions for GV and GDV(Gibb's free energy or free enthalpy)for the systems described above using only the energy and entropy terms considered thus far. (d)Solve for the equilibrium concentrations of vacancies and divacancies, nV/N and nDV/N,respectively.Use Stirling's approximation to simplify your answer: In(p!)=pln(p)-p (e)Sketch the results in(d)as a function of temperature.Briefly discuss the physical reasons for the behavior and possible implications for diffusion. (f)Finally,briefly criticize the model discussing omissions and their possible effects. 3. Plots of the thermal gradient,GL,in the liquid at the liquid-solid interface versus the solidification velocity,R,are frequently used to define the conditions under which the various growth forms of solid solution alloys freeze. (a)Draw a GL versus R diagram for a fixed composition solid solution alloy and identify the various microstructural regions and the location of the structure transition boundaries. (b)Define the major phenomena which account for the various microstructure transitions
1 . The following questions should be answered with rigor. (a) Is it correct to say that the Gibbs energy of a system always decrease as it undergoes change? Why ? Present a statement consistent with thermodynamics. (b) Is it correct to say that the activity of a component must be the same in two mutually equilibrated phases? Why? Formulate an acceptable statement. (c) Can the entropy of an adiabatic system decrease? If so, indicate how you would observe (measure) the entropy change. (d)Can Cp be less than Cv for a stable system? Support your answer? (e) Is it necessary to have an atomistic model to apply thermodynamic arguments? 2. Consider a crystalline solid of N atoms with coordination number Z and cohesive energy Ec. (a) Following a simplified model of the solid that takes into account only nearest-neighbor interactions, write down an expression for the formation energy of a vacancy, EDV. Do the same for a divacancy, EV. Remember to conserve numbers of atoms. (b) Next write down an expression for the configurational or mixing entropy of a system of nV vacancies in the solid. Do the same for a system of nDV divacancies. Remember to count all possible arrangements of the system. Assume that nV and nDV are much less than N. (c) Formulate expressions for GV and GDV (Gibb's free energy or free enthalpy) for the systems described above using only the energy and entropy terms considered thus far. (d) Solve for the equilibrium concentrations of vacancies and divacancies, nV/N and nDV/N, respectively. Use Stirling's approximation to simplify your answer: ln( !) ln( ) p pp = − p (e) Sketch the results in (d) as a function of temperature. Briefly discuss the physical reasons for the behavior and possible implications for diffusion. (f) Finally, briefly criticize the model discussing omissions and their possible effects. 3. Plots of the thermal gradient, GL, in the liquid at the liquid-solid interface versus the solidification velocity, R, are frequently used to define the conditions under which the various growth forms of solid solution alloys freeze. (a) Draw a GL versus R diagram for a fixed composition solid solution alloy and identify the various microstructural regions and the location of the structure transition boundaries. (b) Define the major phenomena which account for the various microstructure transitions
(c)Indicate how the local quench rate,T,varies on the GL-R plot. (d)Describe how the secondary dendrite arm spacing varies with local solidification time,tr,and local quench rate,T. 4. The elements A and B are solids at 1200K and form two solid "stoichiometric"compounds A2B and AB2 at 1200K.B has very limited solubility in A.A has a negligible vapor pressure,but for the sublimation of pure B: B(s)=B(v)AG(joules)=187,000-lIOT R=8.314 J/mol-K The vapor pressure for B over the equilibrated AB2-A2B mixture is given as: 1ogP(atm=.100+6.5 T The vapor pressure for B over the equilibrated A-A2B mixture is given as: 10gP(atm-130o0+7.0 T (i)What are the enthalpy and entropy changes for the sublimation of pure A? (ii)Calculate the standard Gibbs energies of formation for A2B and AB2- (iii)Carefully plot the AG of mixing diagram for the system between pure A and AB2- (iv)What is the activity of B for the two-phase field AB2-A2B? 5. Analyze the thermodynamics and kinetics of reduction of a NiO coupon at 1000K under the following three sets of conditions: (a)Ultra-high vacuum(outer space) (b)Rowing Ar containing 1%H2(1 atm) (c)Flowing H2(1 atm) In each case,predict the rate-limiting-step,and set up some expressions to describe the kinetics.The following standard Gibbs energies of formation at 1300K may be useful: AG Nio =-148,680 joules/mole AG for H20 =-192,540 joules/mole R=8.314 joules/mole-K VNi 6.6cm/mole;VNio 9.24 cm/mole
(c) Indicate how the local quench rate, T, varies on the GL-R plot. (d) Describe how the secondary dendrite arm spacing varies with local solidification time, tf, and local quench rate, T. 4. The elements A and B are solids at 1200K and form two solid "stoichiometric" compounds A2B and AB2 at 1200K. B has very limited solubility in A. A has a negligible vapor pressure, but for the sublimation of pure B: B(s) = B(v) (joules) =187,000-ll0T R = 8.314 J/mol-K 0 ΔG The vapor pressure for B over the equilibrated AB2-A2B mixture is given as: log P(atm) = - 11000 T + 6.5 The vapor pressure for B over the equilibrated A-A2B mixture is given as: l0g P(atm) - - 13000 T + 7.0 (i) What are the enthalpy and entropy changes for the sublimation of pure A? (ii) Calculate the standard Gibbs energies of formation for A2B and AB2- (iii) Carefully plot the AG of mixing diagram for the system between pure A and AB2- (iv) What is the activity of B for the two-phase field AB2-A2B? 5. Analyze the thermodynamics and kinetics of reduction of a NiO coupon at 1000K under the following three sets of conditions: (a) Ultra-high vacuum (outer space) (b) Rowing Ar containing 1% H2 (1 atm) (c) Flowing H2 (1 atm) In each case, predict the rate-limiting-step, and set up some expressions to describe the kinetics. The following standard Gibbs energies of formation at 1300K may be useful: AG°Ni0 = -148,680 joules/mole AG0 for H20 = -192,540 joules/mole R = 8.314 joules/mole-°K VNi = 6.6cm3 /mole; VNi0 = 9.24 cm3 /mole
