Lecture 2 - Kinetic Theory of Gases

Lecture 2 - Kinetic Theory of Gases - Chem 107B TA Office...

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Unformatted text preview: Chem 107B TA Office Hours Chem Annex (Rm 1480A) Libo Li (lili@ucdavis.edu ) Mon 9 noon Benjamin Samudio (bmsamudio@ucdavis.edu ) Tu 9 noon Ying Liu (yixliu@ucdavis.edu ) Wed 9 noon Peiran Chen (prchen@ucdavis.edu ) Th 9 noon Final Exam: Fri March 18 th at 10:30 am in 198 Young Kinetic Theory of Gases Model: Gas consists of large number of molecules far apart on average (~10 23 in 1-liter). Molecules have small size compared to distance from neighbor (100-fold). Collisions between molecules are elastic and random (thermal energy = k B T). No interactions between molecules (no attraction or repulsion). Question: How do we describe macroscopic properties of a gas (e.g. press, vol or temp) in terms of molecular motion (i.e. speed and energy of individual molecules)? PV = Nk B T Goal: Derive an expression for Pressure and Temp in terms of average speed of individual molecules. Work Energy PV Energy (i.e. motion) of gas molecules 2 2 2 z y x v v v v c + + = = Molecular Velocity (v) vs Speed (c) Molecular speed is a scalar quantity and more commonly used. N v v v v v N 2 2 3 2 2 2 1 2 + + + + = K 2 2 2 2 z y x v v v v + + = 3 2 2 2 2 v v v v z y x = = = (isotropic motion) Summary of Kinetic Theory Equations ) ( Law Gas Ideal T Nk PV B = ) ( 3 2 Theory Kinetic v Nm PV = B k v m T 3 2 = M RT m T k v B 3 3 2 = = trans E N PV 3 2 = T k E B trans 2 3 = Translational kinetic energy proportional to PV and Temperature: Mean squared velocity ( ) proportional to PV and Temperature: 2 v Nm PV v 3 2 = Molecular Velocity and Energy Large # of molecules (N = 10-23 ) in 1-liter at 298 K and 1 atm. How do we calculate statistics for velocity and energy? T k E B trans 2 3 = m T k v B 3 2 = Statistics of Speed (c) and Energy (E) Speed (c) Fraction (f(c)) Energy (E) Fraction (f(E)) Boltzmann Maxwell ) exp( ) ( T k E E f B Probability c 1 < c < c 2 : 2 1 ) ( c c dc c f c 1 c 2 Probability E > E a : E a ) 2 exp( ) ( 2...
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Lecture 2 - Kinetic Theory of Gases - Chem 107B TA Office...

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