thermal_3_01_26_2011

thermal_3_01_26_2011 - The Microscopic Underpinnings of the...

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The Microscopic Underpinnings of the Ideal Gas Law Lecture 3
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Caloric Theory Kinetic (atomistic) Theory 1730 Central Question No. 1 : Are atoms convenient, abstract accounting tools or are they real? 1790 Count Rumford Central Question No. 2 : If atoms are real, what do they look like and how do they behave? Bernoulli Change in Thought 1903 Soft, squishy “tennis” balls? Point-like “particles” running about at random? Gibbs “Statistical Mechanics
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Ideal Gas Assumptions – Microscopic Physics 1. A gas is made from a large number of molecules/atoms 2. The gas is comprised of identical molecules 3. The size of individual molecules are very small compared to their average separation distance 4. Molecules obey Newton’s Laws of Motion 5. Molecules do not interact with each other 6. Collisions between molecules and container walls are elastic 7. Motion of molecules is entirely random are most restrictive and limit the Ideal Gas model to low pressure (low density) gasses.
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What we will cover today 1. Microscopic understanding of pressure . ean free path of gas molecules 3. Mean free path of gas molecules 4. Maxwellian distribution of velocities (probability distribution function)
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Review: Average value and rms value Given five numbers: N= {5, 11, 32, 67, -89} N av =<N> = N= = 5.2 5 11 32 67 ( 89) 5 + + + + - 2 2 2 2 Why is the rms value larger than N av ? N av 2 =<N> 2 = N 2 = 2 5 11 32 67 ( 89) 5 + + + + - = 2716 = 52.1 2 2 2 2 2 5 11 32 67 ( 89) 5 + + + + - N rms = N av 2 =
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Can we understand origin of gas pressure from microscopic considerations? ball bearing, mass m, velocity -v y x y p ball = p y (final) – p y (initial) = m | v y | - [ -m | v y |] 2m For elastic collision, magnitude of velocity does not change, so . . . . Scale F = p t = 2m | v y | p scale = - p ball F t t Impulsive Force
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Confine one air molecule into very narrow tube with moveable piston p molecule = p y (final) – p y (initial) = -m | v y | - ( m | v y |) = -2m | v y | For elastic collision, magnitude of velocity does not change, so . . . . Air molecule,
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thermal_3_01_26_2011 - The Microscopic Underpinnings of the...

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