Lecture_03_01_25_2012

Lecture_03_01_25_2012 - The Mi Th Microscopic i...

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The Microscopic Underpinnings of the Ideal Gas Law Ron Reifenberger Birck Nanotechnology Center Purdue University January 25, 2012 Lecture 3 1
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Kinetic Central Question No. 1 : Are atoms convenient, abstract ccounting tools or are they real? Change in Thought Caloric Theory (atomistic) Theory 1730 accounting tools or are they real? Central Question No. 2 : If atoms re real what do they look like Bernoulli 1790 Count Rumford are real, what do they look like and how do they behave? 1903 Soft, squishy “tennis” balls? Hard, point-like “particles” Gibbs “Statistical echanics bouncing about at random? Mechanics 2
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Ideal Gas Assumptions – Microscopic Physics 1. A gas is made from a large number of molecules/atoms he gas is comprised of identical molecules 2. The gas is comprised of identical molecules 3. The size of individual molecules are very small compared to their average separation distance 4. Each molecule obeys Newton’s Laws of Motion 5. The molecules do not interact with each other 6. Collisions between molecules and container walls are elastic 7. Motion of molecules is entirely random Assumptions 3 & 5 are most restrictive and mit the Ideal Gas model to low pressure limit the Ideal Gas model to low pressure (low density) gasses. 3
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What we will cover today 1. Microscopic understanding of pressure 2. Velocity & KE of gas molecules 3. Mean free path of gas molecules axwellian distribution of velocities 4. Maxwellian distribution of velocities (probability distribution function) 4
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Review: Average value and the s” average value rms average value Given five numbers: N= {5, 11, 32, 67, -89} N av =<N> = N= = 5.2 5 11 32 67 ( 89)  5 (N 2 ) av =<N 2 >= N 2 = 22 2 2 2 5 11 32 67 ( 89)  = 2716 5 2716 2 2 2 11 32 67 ( 89) not 25 !! = 52.1 5 5 N rms = (N 2 ) av = Why is the rms value larger than N av ? 5
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Can we understand origin of gas pressure from microscopic considerations? ball bearing, mass m, velocity -v y y For elastic collision, magnitude of velocity does not change, so . . . . x p ball = p y (final) – p y (initial) m - - Force Scale = m | v y | [ m | v y |] = 2m | v y | p scale = - p ball F = p t F t t Impulsive Force 6
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Confine one air molecule into very narrow tube with moveable piston Moveable piston with rea A For elastic collision, magnitude of velocity does not change, so . . . .
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This note was uploaded on 02/05/2012 for the course PHYS 242 taught by Professor Staff during the Spring '08 term at Purdue.

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Lecture_03_01_25_2012 - The Mi Th Microscopic i...

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