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Unformatted text preview: 1 Thermodynamics Gangkhar Puensum 2 Molecular Speeds The average kinetic energy per mole of gas is given by: Is the root mean square or RMS velocity. 2 u RT u M U 2 3 2 2 1 = = M RT u M RT u 3 or 3 2 2 = = 3 Examples Compare the kinetic energies and speeds of oxygen and hydrogen: 4 2 32 2 2 2 2 2 2 = = = H O O H MW MW u u What is the RMS speed of ammonia at 25 C? 1 2 ms 660 017 . 298 314 . 8 3 3 3 3 = = = NH NH MW RT u 4 How fast is that? Pretty fast! 660 meters per second converts to 1480 m.p.h. (or mach 1.9) So how come I dont start coughing almost immediately when a flask of ammonia is released at the back of the class? 5 Molecular Collisions Because molecules (or atoms) collide! From what we know already we can consider: The number of collisions per molecule per unit time Total number of collisions Distance between collisions Consider two particles A and B 6 A Requirements for a Collision B A u Radius = r A + r B 7 Requirements for a Collision The radii of these particles is r A and r B . For now only particle A moves, and it moves with an average velocity of u A . In 1 second the particle will move u A meters. There will be a collision anytime there is a B particle closer than the sum of the two radii, i.e. r AB . If the center of a B particle is within the cylinder there will be a collision. 8 Collision Frequency The volume of the imaginary cylinder is given by: A AB u r 2 If N B is the total number of B molecules, the number per unit volume is N B /V and the number in the cylinder per unit time is: A B A AB Z V N u r = 2 The Collision Frequency This is the number of collisions experienced by A in unit time. 9 Comment This is a little artificial since we are considering only how many collisions an A particle makes with B particles. Maybe more interesting is the total number of A B collisions the collision density. 10 Collision Density The total number of A molecules per unit volume is N A /V then the total number of A B collisions per unit time, per unit volume is simply the collision frequency times N A /V, i.e. 2 2 V N N u r Z B A A AB AB = 11 Collision Density Z AB is the collision density or number. The units are: 1 3 6 2 2 2 = = = s m sm m m V N N u r Z A B A AB AB 12 In a Gas of Pure A If all the particles are A particles the equation becomes: 2 2 2 2 2 2 2 2 V N u d V N u r...
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 Fall '10
 CONSORS
 Mole

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