MAT E 640
Advanced Thermodynamics in Materials
Department of Chemical and Materials Engineering
Final Exam
December 18, 2020
1. Choose whether the following statements are true or false. If a statement is false, explain why? [20]
T F The enthalpy of mixing in both ideal solution and regular solution is independent of temperature.
T F The Le Chatelier’s principle states when subjected to an external influence, state of system shift in that direction which tends to enlarge the effects of external influence.
T F For an incompressible substance, the specific heat at constant pressure is identical with the specific heat at constant volume.
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 is the same as the molar property of its pure component.
T F Consider the liquid-vapor saturation curve of a single-component substance on the P-T diagram. The slope of this curve at any point is proportional to the entropy change and inversely proportional to the volume change at that point.
T F When A-B solution shows negative 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, it is impossible to liquefy the gas by compression above the critical pressure.
2. Multiple Choice - Circle ONE correct answer for each. (16 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 of the following figures illustrate the correct dependence of the molar Gibbs free energy on the temperature at constant pressure for a solid?
iii) Which constraints must be imposed on system to make the Helmholtz function decrease?
a) constant T and P
b) constant U and T
c) constant U and V
d) constant T and V
iv) In a P-T diagram, the slopes of sublimation and vaporization curves for all substances are
a) negative
b) positive
c) zero
d) none of the mentioned
v) 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
vi) The applicability of the assumption of regular solution to a real system increases if the system has
a) large W and at low temperature
b) small W and at low temperature
c) large W and at high temperature
d) small W and at high temperature
vii) What is the configurational entropy of 5 moles of CH3F at absolute zero K?
a) 57.6 J·K-1 b) 11.5 J·K-1 c) 45.6 J·K-1 d) 9.12 J·K-1 e) 0 J·K-1
viii) 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) high temperature and low pressure
c) low temperature and low pressure
d) high temperature and high pressure
3. In the following binary system, the Helmholtz free energy of mixing is given by
DA = ax1x2
2 J/mole where a is a constant
Calculate ∆A1 and ∆A2. (10 Marks)
4. Justify the following statement: if species A behaves ideally over the entire composition range of an A-B binary solution, then species B also behaves ideally. (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. (9 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. The Fe-Cr binary phase diagram is given below. Assuming regular solution behavior. for liquid solution and regular solution behavior. for solid solution. Predict Ωs and Ωl. (10 Marks)
∆Hm (Fe) = 15, 200 J/mole at melting point of Fe
∆Hm (Cr) = 17, 200 J/mole at melting point of Cr
AFe =55.85 g/mole, A Cr=52.0 g/mole
Assume ΔHm and ΔSm do not vary with T.
8. For the Al-Ca phase diagram given below draw schematics of plausible molar free energy curves showing the common tangent construction as a function of composition, xCa, at T1 = 900 °C, T2 = 640 °C, T3 = 549 °C and T4 = 500 °C. (20 Marks)