[SOLVED] MAT E 640 Advanced Thermodynamics in Materials 2021 R

MAT E 640

Advanced Thermodynamics in Materials

Department of Chemical and Materials Engineering

Deferred Final Exam

January 20, 2021  180 minutes

Answer all questions.  State any assumptions you make and explain your answers. The total number of marks is 90.

1. Choose whether the following statements are true or false. If a statement is false, explain why? [10]

T    F The enthalpy of mixing in ideal solution is independent of temperature, while

the enthalpy of mixing in regular solution depends on temperature.

T    F In a typical phase diagram, as temperature decreases, the Gibbs free energy of

both solid and liquid solution as a function of composition also decreases.

T    F The partial molar value of an extensive property in a mixture of ideal gases is

the same as the molar property of its pure component.

T    F When A-B solution shows positive deviation from Raoult’s law, A-A and B-B

components are more likely forming clusters in solution.

T    F For a non-ideal gas, molar volume of vapor and liquid keep constant during

transformation from vapor to liquid below the critical pressure.

2. Multiple Choice – Circle ONE correct answer for each. (10 marks)

i) Which of the following is true for the heat and work during a thermodynamic process?

a) q for reversible < q for irreversible and work for reversible > work for irreversible

b) q for reversible > q for irreversible and work for reversible > work for irreversible

c) q for reversible > q for irreversible and work for reversible < work for irreversible

d) q for reversible < q for irreversible and work for reversible < work for irreversible

ii) Which constraints must be imposed on system to make the Gibbs function decrease?

a) constant T and P

b) constant U and T

c) constant U and V

d) constant T and V

iii) During phase transitions like vaporization, melting and sublimation

a) pressure and temperature remains constant

b) volume and entropy changes

c) both of the mentioned

d) none of the mentioned

iv) What is the configurational entropy of 5 moles of CH3Cl at absolute zero K?

a)   0 J·K-1           b) 57.6 J·K-1       c) 11.5 J·K-1         d) 45.6 J·K-1        e) 9.12 J·K-1

v) The van der Waals equation is the equation of state for a non-ideal gas. The properties of a gas predicted by this equation are different from that of an ideal gas. Under what two conditions are the properties of a real gas expected to be the most non-ideal?

a) low temperature and high pressure

b) low temperature and low pressure

c) high temperature and high pressure

d) high temperature and low pressure

3. Shown below is the free energy of mixing diagram for liquid and solid solutions of a binary A-B system at temperature T1. (assuming △sm(o),A =△sm(o),B )

a) Is T1 greater than, less than or equal to the melting temperatures for pure A and pure B?  (5 Marks)

b) Which element has the higher melting point? (5 Marks)

c) This system exhibits a positive deviation from ideal behaviour for both the liquid and solid solutions. Which solution (liquid or solid) has the larger enthalpy of mixing? (5 Marks)

4. Briefly explain the difference in the phase separation due to composition fluctuation within the miscibility gap in the cases between

i)  alloy composition within binode region but outside of spinode region, and

ii) alloy composition within spinode region

(hint: compare free energy change, morphology difference, etc) (10 Marks)

5. For sulfur dioxide, Tcr  = 430.7 K and Pcr  = 77.8 atm. Calculate

a) The critical van der Waals constants for the gas.

b) The critical volume of van der Waals SO2,

c) The pressure exerted by 1 mole of SO2  occupying a volume of 500 cm3  at 500 K.

Compare this with the pressure which would be exerted by an ideal gas occupying the same molar volume at the same temperature. (10 Marks)

6. In the P–V diagram, sketch a typical isotherm for a van der Waals gas at temperature below critical temperature. Label the equilibrium pressure as accurate as possible. (5 Marks)

7. A  binary  phase  diagram  is  given  below.  Predict  the  Ωl and  estimate  the  heat (enthalpy) of melting for pure Li. (10 Marks)

8. For the Mg-Pb phase diagram given below draw schematics of plausible molar free energy curves showing the common tangent construction as a function of composition, xPb, at T = 600 。C, T = 455 。C, T = 250 。C, and T = 100 。C.  (20 Marks)