Winter Term 2013 AERO 532: MOLECULAR GAS DYNAMICS

MID-TERM EXAM

Open notes, open book, no wireless devices, answer all questions.

Sign the pledge: "I have neither given nor received aid on this examination."

Points for each question are given in []. 1. A chemical reactor produces atomic carbon vapor at a temperature of

1000 K and a pressure of 0.1 N/m2 that flows horizontally over a flat, solid surface with a streamwise length of 1 cm (carbon has a weight of 12 g/g-mol, assume hard sphere diameter of 4x10-10 m). (a) Determine the regime of this flow. (b) The sticking coefficient of carbon (probability that an atom adheres to the surface) is 0.1. Calculate the net mass flux to the surface. (c) Calculate the net surface pressure assuming fully diffuse reflection and a surface temperature of 300 K. [35]

2. The Variable Hard Sphere model (VHS) is employed in engineering for simulating collisions. In this model, the total collision cross section is:

σdΩ = σ o0

4π

∫ g−2ω where σo is a constant, g is the relative velocity, and ω is a molecular parameter (when ω =0, we have the hard sphere model). Using equilibrium kinetic theory, determine the molecular collision rate between particles of species A and B. Deduce the mean free path for a simple gas. Hint: you will need to use the gamma function:

Γ(x) = t x− 1 exp(−t)dt0

∞

∫ [30]

3. (a) Consider the following one-dimensional wave function for x in [0,1]:

Ψ = x2 exp(-iωt)

Determine the normalized wave function, average position, and average energy. (b) For N2 molecules, how many rotational levels exist between the ground and first vibrational levels (assume rigid rotor with θr=2.9 K and harmonic oscillator with θv=3,390 K). (c) Write down all information for the following electronic states: (i) N: 3d 4F (ii) N2

-: X 2Πg [35]

Grader’s Notes – AERO532 Midterm Exam

April 2, 2013

Two points were deducted for each mathematical error, if the method used to solve the question

was sound. Please remember when doing your assignments that if the grader cannot read your

work, he/she cannot assign you partial credit in the event of an incorrect answer. The average

grade for the midterm is 65.6 with a standard deviation of 18.8.

Q1

(35 points) Many students assumed that the reflected number density is equal to

instead of the correct value of

. Few students also

incorrectly used instead of the correct .

Q2

(30 points) Most students had difficulties with this problem. Students used either the wrong

definition/equation of the collision rate or failed to correctly perform the integration. Five points

were awarded for writing down the correct definition of the collision rate and another five points

for the definition of the mean free path.

Q3

(35 points) Several students used the wrong spacing between the ground and first vibrational

levels of

instead of the correct spacing in Part (b).

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