PolyatomicMoleculesLect20ME501F2011

# PolyatomicMoleculesLect20ME501F2011 - Purdue University ME...

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Patterned Border Template 1 Purdue University School of Mechanical Engineering ME 501: Statistical Thermodynamics Lecture 20: Calculation of Thermodynamic Properties for Polyatomic Molecules Prof. Robert P. Lucht Room 2204, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana [email protected] , 765-494-5623 (Phone) October 24, 2011

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Patterned Border Template 2 Purdue University School of Mechanical Engineering Lecture Topics • Rotational modes and contribution to thermodynamic properties for polyatomic molecules. • Normal modes of vibration for polyatomic molecules. • Vibrational contribution to thermodynamic properties for polyatomic molecules. • Electronic contribution to thermodynamic properties for polyatomic molecules.
Patterned Border Template 3 Purdue University School of Mechanical Engineering Rotational Modes for Polyatomic Molecules • For a linear polyatomic molecule the degrees of freedom for the rotational mode are the same as for a diatomic molecule. The rotational partition function is also the same: where 2 2 2 8 e rot e i i i BB e hcB h I mx kk I  where I e is the moment of inertia, m i is the mass of each nucleus i in the linear polyatomic molecule, and x i is the distance of the nucleus i from the center of mass of the molecule. The factor is 1 for a non- symmetric polyatomic molecule (N 2 O = N-N-O) and 2 for a symmetric molecule (CO 2 = O-C-O, C 2 H 2 = H-C-C-H). 1 rot rot Z    

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Patterned Border Template 4 Purdue University School of Mechanical Engineering Rotational Modes for Polyatomic Molecules • For a linear polyatomic molecule the contribution of the rotational mode to the assembly properties is exactly the same as for a diatomic molecule. For T >> rot : v, , ln rot rot rot C rot p rot rot rot rot rot eu hR T cR Z T sR T R Z R R T          
Patterned Border Template 5 Purdue University School of Mechanical Engineering • For a non-linear polyatomic molecule there is an additional degree of freedom for the rotational mode. The analysis of the rotational motion is very complicated (even the classical analysis). For each nonlinear

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PolyatomicMoleculesLect20ME501F2011 - Purdue University ME...

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