[試題] 101-2 陳振中 物理化學三 期中考
課程名稱︰物理化學三
課程性質︰化學系五選三必修
課程教師︰陳振中
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰4/12
考試時限（分鐘）：110min+20min延長
是否需發放獎勵金：是
試題 :
Physical Chemistry(III) - APR 12 2013
1. Calculation:
(a)Using the Boltzmann distribution to calculate the ratio of populations at
298K of energy levels seperated by 100cm^-1 and 10 kJ/mol (各10分)
(b)Calculate the translational partition function for H2(g) (2amu) at 1000K and
1 bar (1 bar = 100000Pa = 750.0616827 Torr) (10分)
(c)What is the thermal wavelength Λ for a htdrogen atom at 2 K? (10分)
(有給：亞佛加厥常數NA、波茲曼常數k、理想氣體常數R、普朗克常數h)
2.Suppose we have a canonical emsemble partition function of the following form
: Q(V)αV^n
(a)If the system is an ideal gas or real gas, explain what n should be (10分)
(b)The partition function for a mixture fo two monoatomic ideal gases is given
by
N1 N2
q1 q2
Q = ------
N1!N2!
∂lnQ
Starting with P = kT(-------) ※N1 N2 T fixed,
∂V
derive the ideal gas law: PV=(n1+n2)RT (10分)
3.The rotational energy of a rigid diatomic molecule is given as
J(J+1)h^2
E = --------
8π^2I
Here J is the rotaitonal quantum number, and I is the moment of inertia of the
diatomic molecule.
(a)Write down the rotaitonal partition function for a molecule at T<<Θr (10分)
(b)Prove that the rotational partition function for a molecule at T>>Θr is
8π^2IkT
q = -------- (10分)
σh^2
__
4 For a system of N particles, suppose we have E=Nε, where ε is the energy of
a single particle, N is the number fo particles, and E is the system energy.
__
(a)What is the implicit assumption to have E=Nε valid? (4分)
(b)Startion from Q = Σ exp(-Ei/kT), where Ei refers to the energy when the
i
system is in the ith state, determine the probability that a molecule is in the
jth energy state (πj) (8分)
__
(c)Compare the fluctuations in ε, i.e. σ(ε)/ε and that in E, i.e. σ(E)/E.
What conclusion can you draw? (8分)
__
[Hints: you can use the relation ΣpiEi^2 = kT^2 (∂E/∂T)※N,V fixed + E^2
without proof, where pi is the probability that the system is in the ith state]
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