MS 501200
Final Exam
2021-6-17
Answer questions only in English.
1. Answer the following questions with “〇” for true and “X” for false. If it is false, you MUST explain why it is
false to get the points. If you do not explain or your explanation is not reasonable, you would NOT get the
points. (2 points for each)
(1) H is a state function.
(2) E = 0 for every cyclic process.
(3) If a closed system at rest in the absence of external fields undergoes an adiabatic process that has w = 0, then
the system’s temperature must remain constant.
(4) For every process in an isolated system, S = 0.
(5) CP – CV = R for all gases.
(6) G is always zero for a reversible process in a closed system capable of P-V work only.
(7) The work done by a closed system can exceed the decrease in the system’s internal energy.
(8) Gsys + Gsur is constant for any process.
(9) Ssys + Ssur is positive for every irreversible process.
(10) The entropy S of a closed system with P-V work only is always maximized at equilibrium.
2. Make use of the total differentials of energy quantities and the Maxwell’s relations, derive the following terms
in terms of , , V, T, P, and CP. Give the value of each term for one mole of a monatomic ideal gas at 1000 K
and 2000 atm. (10%)
(a) (P/T)S
(b) How does a reversible adiabatic increase in pressure affect the enthalpy of a substance?
3. Explain why the work done by the system in a reversible process is a maximum. If this work is performed at a
constant temperature, it would be equivalent to the decrease of the Helmholtz free energy. (10%)
4. Plot a schematic phase diagram for H2O with the triple point at 0.01 oC and 4.6 torr and critical point at 374 oC
and 218 atm. Based on the phase diagram, plot the free energy curves for the three phases at 1 atm. Explain
why water normally cannot transform to ice at 0 oC and the supercooled water at –10 oC has a higher tendency
to transform to ice than that at -5 oC. Justify that the tendency is approximately proportional to the magnitude
of supercooling T. (10%)
5. Calculate the vapor pressure of droplets of water in a diameter of 10-5 cm at 25 oC. What is the vapor-pressure
ratio for these droplets to that of a plane surface of water? The surface energy of water (erg/cm2 or J/m2) is for
you to find out. (10%)
6. Describe how hydrogen fugacity can be measured by electrochemical method. (10%)
7. What is a Wulff plot? How can it be applied to predict the shape of single crystals? (10%)
8. The melting point of gold is 1064 oC. However, gold may melt at below 500 oC when it is in the form of
nanoparticles. Explain this phenomenon and propose two models to explain this difference. (10%)
9. The Fe-Cr phase diagram is shown below. Iron has a bcc structure (α) at low temperatures, which transforms to
an fcc structure (γ) at 911 oC and then transforms back to the bcc structure at 1396 oC, while Cr maintains a bcc
structure throughout. Copy the following figure and label the single-phase and two-phase fields with alphabets
on the phase diagram. Indicate the three kinds of congruent melting. Is Hmix (solid) positive or negative for
this system? (10%)
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