Chemical and Materials Engineering
MAT E 640
Advanced Materials Thermodynamics
Midterm Examination
25% of Final Grade
October 20, 2020
12:30-1:50 PM
Tips
Read through the entire test first before starting the exam.
Do not leave blanks - attempt all problems, you cannot get marks for blanks.
Read carefully and be sure you answer what is being asked.
Give concise answers. State any assumptions you make.
Marks
Marks for each part of the question are shown in the question as [X]. The total number of marks is 90.
1. Choose whether the following statements are true or false. If a statement is false, explain why? [20]
T F The enthalpy and internal energy of an ideal gas only depend on the temperature of the system.
T F With the same undercooling, the heterogeneous nucleation requires smaller
critical nuclei size and lower energy barrier than the homogeneous nucleation.
T F Based on the first law of thermodynamics, energy is always conserved, while entropy could be created.
T F At constant composition and entropy, the enthalpy will decrease as pressure increases.
T F The reason to form. coherent embryo is that minimizing interfacial energy is more important than minimizing strain energy.
T F In an adiabatic expansion of an ideal gas the temperature always goes up.
2. One mole of a diatomic ideal gas is subjected to the following sequence of steps:
(a) Starting at 300K and 1 atm, the gas is heated reversibly to 600K at constant volume.
(b) The gas is reversibly expanded at constant temperature until its volume is again doubled.
(c) The gas is then reversibly cooled to 300K at constant pressure.
(d) The gas finally expands freely into a vacuum to double its volume.
Calculate the values of q and w and the changes in U, H, and S for each step. [20]
3. A hypothetic system with two available energy levels ε0 and ε 1 is populated by N particles at constant temperature T.
(a) Calculate the average energy per particle. [5]
(b) Calculate the entropy of the system with N particles. [5]
4. Show [5]
5. Below is the crystal structure of wurtzite ZnS (yellow is Zn and grey is S). What is the total configurational entropy in each of following question? (Note: the total number of sublattice sites for Zn is NA)
(a) A perfectly ordered wurtzite ZnS crystal (with no defects), as shown below. [5]
(b) A perfectly ordered wurtzite ZnS crystal, but with one vacancy on the sublattice of Zn atoms and one vacancy on the sublattice of S atoms. [5]
(c) A perfectly ordered wurtzite ZnS crystal, but with one extra S atom substitutes the sublattice of Zn atoms. [5]
(d) A perfectly ordered wurtzite ZnS crystal, but with one nearest neighbor Zn and S atoms exchanged position. [5]
6. Draw schematic G-P curves which would be consistent with the iron T-P diagram shown as below at the temperatures 400, 600, and 1600°C. Neglect the δ phase. [15]