110c-lecture23

# 110c-lecture23 - Midterm 2 range 53 – 89 mean 72 std dev...

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

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Midterm 2 range 53 – 89. mean 72. std dev 10 exams returned in Tue discussion session. Problem Set #5 Due Wed June 2 nd . Final Exam Tue June 8 th at 1:00-3:00 pm in 1006 Giedt. Chapters 19 – 29? Chapter 27: Kinetic Theory of Gases Model: • Gas consists of large number of molecules far apart on average (10 23 in 22- ℓ at 0 ºC ). • Molecules have small size compared to distance from neighbor (100-fold apart). • 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 Objective: • Derive an expression for Pressure and Temp in terms of average speed of individual molecules. Work Energy Pressure and Temp vs Velocity What is Force exerted by single molecule? ( ) x x x mu mu mu momentum 2 = − − = Δ x u a velocity ce dis t / 2 / tan = = Δ a mu u a mu t momentum F x x x 2 / 2 2 ) ( = = Δ Δ = V mu abc mu bc a mu bc F P x x x 2 2 2 / = = = = Pressure by N molecules in the box: 2 1 2 1 2 x N j jx N j jx tot u N V m u V m V mu P = ∑ = ∑ = = = 2 x tot u mN V P = ⇒ T Nk u mN B x = 2 (single molecule) Ideal gas is isotropic ( = = ) 2 x u 2 y u 2 z u a mu t momentum on accelerati mass F x 2 ) ( = Δ Δ = × = ) ( gas Ideal T Nk PV B = ) ( 2 Theory Kinetic u Nm PV x = m T k u B x = 2 m T k u u u u B z y x 3 2 2 2 2 = + + = m T k u B 3 2 = Statistics of Speed (c) and Energy (E) Speed (c) Prob Density (f(c)) Energy (E) Prob Density (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 − α ) exp( ) ( T k E dE E f B a E a − = ∫ ∞ Mean Speed (<c>): ∫ ∞ = = ) ( dc c cf c c Mean Energy (<E>): ∫ ∞ = = ) ( dE E Ef E E Maxwell Distribution of Molecular Speed...
View Full Document

## This note was uploaded on 06/22/2010 for the course CHEM 21360 taught by Professor Ame during the Spring '09 term at East Los Angeles College.

### Page1 / 17

110c-lecture23 - Midterm 2 range 53 – 89 mean 72 std dev...

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

View Full Document
Ask a homework question - tutors are online