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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 1:003:00 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 at 0 C ). Molecules have small size compared to distance from neighbor (100fold 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 = = x u a velocity ce dis t / 2 / tan = = a mu u a mu t momentum F x x x 2 / 2 2 ) ( = = = 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 ) ( = = = ) ( 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 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>): = = ) ( dc c cf c c Mean Energy (<E>): = = ) ( dE E Ef E E Maxwell Distribution of Molecular Speed...
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 Spring '09
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