Chapter 14 (III)

Chapter 14 (III) - 3. Most probable speed v m 4. The...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
14.5 Maxwell Distribution of Molecular Speeds , ) ( ) ( , ) ( ) ( ) ( / / kT kT e Z N d g d N e Z N d g d N f ε = = = . ) 2 ( 2 / 3 2 h mkT V Z π = Now, we want to apply Maxwell-Boltzman distribution of particles among energy levels to the speed distribution of an ideal gas. From M-B stat., we have where N( ε )d ε is the number of molecules in the energy range of ε to ε +d ε . For an ideal gas, . 2 4 ) ( 2 / 1 2 / 3 3 d m h V d g =
Background image of page 1

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

View Full DocumentRight Arrow Icon
. ) 2 ( 2 4 ) 2 ( 2 4 ) ( / 2 / 1 2 / 3 / 2 / 3 2 2 / 1 2 / 3 3 ε π d e kT N e mkT h V N d m h V d N kT kT = × = Since the number of molecules in the speed range of v to v+dv is given by This is the Maxwell speed distribution, which can also be obtained from the kinetic theory. , 2 1 . 2 , 2 1 2 2 / 3 2 / 1 2 / 1 2 dv v m mvdv v m d mv = = = . ) 2 ( 4 2 1 ) 2 ( 2 4 ) ( 2 / 2 2 / 3 2 2 / 3 2 / 2 / 3 2 2 dv e v kT m N dv v m e kT N dv v N kT mv kT mv = = (14.15)
Background image of page 2
Eq(14.15) satisfies . ) ( 0 N dv v N = N dv v N v v n n 0 ) ( (1)The mean speed (2)The root of mean square speed v rms . 8 ) 2 ( 2 1 ) 2 ( 4 ) 2 ( 4 2 2 / 3 0 2 / 3 2 / 3 2 m kT m kT kT m dv e v kT m v kT mv π = × = = . 3 ] ) 2 ( 8 3 ) 2 ( 4 [ ] ) 2 ( 4 [ 2 / 1 2 / 5 2 / 3 2 / 1 0 2 / 4 2 / 3 2 2 m kT m kT kT m dv e v kT m v v kT mv rms = × = = =
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3. Most probable speed v m 4. The molecular flux --the number of molecules striking a unit area per unit time 5. Equipartition of energy The average energy of a molecule is given by where f is the number of degrees of freedom of its motion (f=3 for a monatomic gas). . 2 , ) ( ) ( 2 / 2 2 m kT v e v dv d dv v dN m kT mv = = = . 8 4 1 4 1 m kT n v n = = , 2 kT f = Assignment #5: 14-1; 14-3; 14-6; 14-8 (Due on Monday, Feb. 8th)...
View Full Document

This note was uploaded on 02/28/2011 for the course PHYS 359 taught by Professor Dr.asdas during the Winter '10 term at Waterloo.

Page1 / 5

Chapter 14 (III) - 3. Most probable speed v m 4. The...

This preview shows document pages 1 - 5. Sign up to view the full document.

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