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jacklu

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[求助] 求解3道热力学题

在美国留学的一个同学的作业题，时间紧迫，发在这里求高人相助。第一题据说最难。写100金币只是为了说明时间的迫切，此题的重要，如果真的做出来了，奖励不以此为下限。要求是，今天（11月26日）下午2点之前须交出结果，时间一过，此题失效！

1. Consider each of the following systems to be “statistically ideal;” in the sense of random mixing of indicated ions on each sublattice with no correlation between occupancies on different sublattices.  In each case find analytical expressions for (a) the configurational entropy of mixing, (b) the partial molar entropy of mixing of each component, and (c) the activity of each component in terms of the mole fraction, x, of the second component in each pair.  Plot these as a function of composition.

a. A perovskite solid solution along the CaTiO3 - CaNbO2N join, where Ca ions occupy the 12-fold cation sites, Ti and Nb occupy the octahedral sites, and O and N occupy the anion sublattice.  Assume that the anions in CaNbO2N are disordered.

b. GaN - CdTe semiconductor solid solutions, assuming cations and anions do not mix, but the mixing of cations with cations and anions with anions is random.

c. Cubic solid solutions along the ZrO2 - Y2O3 join.  The substitution of Y for Zr is compensated by oxygen vacancy formation.  These materials are important solid electrolytes.  Assume that Zr and Y mix at random, and independently of the random mixing of oxide ions and vacancies.

d. The system in (c) shows a maximum ionic conductivity at Y / (Y + Zr) = 0.12.  What does this suggest about the assumptions made above?

2. In a system A - B, the activity of B at 1000 K is given as follows:

XB aB
0.1 0.05
0.2 0.10
0.3 0.22
0.4 0.33
0.5 0.45
0.6 0.56
0.7 0.67
0.8 0.78
0.9 0.89

Plot the activity of both components versus mole fraction after doing the Gibbs-Duhem integration, either numerically or by fitting appropriate equations to the activity.  Calculate and plot the total free energy of mixing and the excess free energy of mixing.  Is this system approximately an ideal solution, a regular solution, or a subregular solution?  Does it deviate positively or negatively from ideality and what are the appropriate parameters describing this deviation?
3. A binary system A - B has the following characteristics:

Melting point of A is 1000 K, heat of fusion is 25 kJ/mol.
Melting point of B is 1500 K, heat of fusion is 40 kJ/mol.
Boiling point of A is 2000 K, heat of vaporization is 200 kJ/mol.
Boiling point of B is 2500 K, heat of vaporization is 250 kJ/mol.
The gases are ideal, and they mix ideally.
The liquid phase is ideal.
The solid phase shows negligible solid solubility.

Calculate and plot the phase diagram from 500 to 3000 K at one atmosphere.  Describe what happens (in terms of phases present) as a mixture containing 60 mole % B is cooled from 3000 to 500 K.

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