[試題] 陸駿逸 物理化學一 期末考

[Derver (木律)]

課程名稱︰物理化學一─熱力學
課程性質︰必修
課程教師︰陸駿逸
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰2013/01/11
考試時限（分鐘）：130
是否需發放獎勵金：是
（如未明確表示，則不予發放）

試題 :

1.Boltzmann said that S = k_B ln(Ω), whereas Gibbs' entropy says

  S = -k_B ΣP_i ln(P_i) where P_i indicates the apperaing probability of the

  microstate i. Explain when do you use the former and when to use the latter.

2.On the top of Jade mountain, the pressure is only 0.6 atm. Estimate the

  boiling point there. The heat of vaporization is 41kJ/mol.

3.When you boil a liquid on an oven, often the boiling bubbles start to appear

  at a temperatiure which is slightly higher than the reported boiling. In

  terms of the Laplace pressure, explain the discrepancy.

4.Suppose tha a non-ideal gas obeys the van der Waals equation of state
       _    _
  (P+a/V^2)(V-b) = RT. Microscopically the potential energy between two gas

  molecules isapproximated as the following form:

  V(r) ┴
       │  │
       │  │
       │  │
       │ 1│  2   3
       ├─┼──────────├
       │  │      │          r(Å)
-0.1eV ┼  │  ┌─┘
       │  │  │
-0.2eV ┼  └─┘
       │
  (a)Calculate the constant a and b.

  (b)Estimate the location (T_c,P_c) of the gas/liquid critical point.

5.Consider a string of atoms which form one dimensional lattice. The molecular

  mass is 100 g/mol.The distance between the neighboring atoms is 2Å, and the

  potential between the neighboring atoms can be described by Hookian spring

  with a spring constant k_s = 100eV/nm^2. The longitudinal vibrations of these

  atoms form the sound wave. Ignore the transverse vibrations in this exam

  question.

  (a)Plot the vibration frequency as the function of the (1d) wave vector

     k = 2π/wavelength.

  (b)How does the heat capacity of this system change with the temperature at

     low temperature? Explain your reasoning.

  (c)Estimate the characteristic (Debye) temperature for this system. (Above

     this characteristic temperature, the heat capacity will be roughly a

     constant.)

6.Einstein's solid model predicts a heat capacity which does not depend on the

  dimensionality of the solid. The heat capacity of the Debye's solid model,

  however, depends strongly on the dimensionality of the solid. Explain the

  main reason which makes the difference.

7.Suppose that you have an equilibrium crystal, whose shape obeys the Wulff

  construction rule. The cross section of the crystal has the following shape,

  where L1:L2:L3=2:√2:1. All the angles are 3π/4. Suppose that the surface

  energy γ1 = 1J/m^2. What are the values for γ2 and γ3?


        γ1
   /──────\  γ2
  /     L1    L2 \
 │              │
 │           L3 │ γ3
  \              /
   \──────/

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