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

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Chem 107B TA Office Hours
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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. 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 = nRT PV Energy (i.e. motion) of gas molecules Goal: Derive an expression for Pressure and Temp in terms of average speed of individual molecules. Work Energy
Background image of page 2
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 =
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 α 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 2 T k mc c c f B ) exp( ) ( T k E dE E f B a E a = Mean Speed (<c>): = = 0 ) ( dc c cf c c Mean Energy (<E>): = = 0 ) ( dE E Ef E E
Background image of page 4
Maxwell Distribution of Speed T k mc B B e T k m c c f 2 2 3 2 2 2 4 ) ( = π v = velocity, has a direction (vector) c = speed, no direction (scalar) Fraction of molecules (dN/N) with speeds c to c+dc: Maxwell Distribution 2 2 2 z y x v v v c + + = dc e T k m c N dN T k mc B B 2 2 3 2 2 2 4 = = 2 1 ) ( c c dc c f N dN Mean Speed (<c>): = = 0 ) ( dc c cf c c
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Average Molecular Speed ( ) T k mc B B e T k m c c f 2 2 3 2 2 2 4 ) ( = π = 0 ) ( dc c cf c dc e c T k m c T k mc B B = 0 2 3 2 3 2 2 4 From integral table: 2 2 0 3 2 1 a dx e x ax = In our case: T k m a B 2 = and thus M RT m T k c B ππ 8 8 = = 2 2 3 2 2 1 2 4 = T k m T k m B B where R = N A k B and M = mN A c c or c =
Background image of page 6
rms ) T k mc B B e T k m c c f 2 2 3 2 2 2 4 ) ( = π From integral table: In our case, T k m a B 2 = M RT m T k c B rms 3 3 = = 5 2 0 4 8 3 a dx e x ax = [] 2 / 1 0 2 2 / 1 2 ) ( = = dc c f c c c rms 2 / 1 0 2 2 4 2 3 2 4 = dc e c T k m c T B k mc B rms 2 / 1 5 2 3 2 8 3 2 4 = T k m T k m B B where R = N A k B and M = mN A
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/20/2010 for the course CHE CHE 118A taught by Professor Lievens during the Winter '08 term at UC Davis.

Page1 / 34

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

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online