课程名称︰物理化学三 课程性质︰化学系五选三必修 课程教师︰陈振中 开课学院：理学院 开课系所︰化学系 考试日期（年月日）︰4/12 考试时限（分钟）：110min+20min延长 是否需发放奖励金：是 试题 : 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) (有给：亚佛加厥常数NA、波兹曼常数k、理想气体常数R、普朗克常数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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