2303_-_Spr_2011_-_Week_3_-_Kinetic_Theory_-_C

2303_-_Spr_2011_-_Week_3_-_Kinetic_Theory_-_C - The...

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The Molecular Basis of Thermal Physics
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Week 3 – 1 Kinetic Theory of Gases Agenda Homework Review Kinetic Theory of Gases Pressure Temperature Reading: 19.1 – 19.2 22
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3 Kinetic Theory of Gases Microscopic model of an ideal gas based on classical physics. Relate the motion of the molecules in a gas to the temperature and pressure. The model is statistical in nature (number of particles > 1023). Although individual molecular motions are random, we can understand gases very well through their bulk properties. The molecules are constantly moving around in random directions with a distribution of speeds.
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4 There are a very large number of molecules in a typical volume of gas. We know that for ideal gas at STP, 1 mole (6x1023 molecules) occupies 22 L. The molecules are relatively far apart [ compared to size ] The volume for each molecule at STP Vspace = (22.4 x 10-3 m3) / 6 x 1023 o 4 x 10-26 m3 d = V1/3 d ° 3 nm = 3 x 10-9 m Typical molecule has radius r ° 1.5 x 10-10 m = 0.15 nm d / r ° 20 Kinetic Theory of Gases
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5 Kinetic theory of gases Collisions will be elastic. Hard sphere repulsion at short range (0.3 nm spacing). Weak interactions at longer range (> 3 nm spacing). Van der Waals interaction energy for N2 molecules – Virginia University Molecule – molecule interaction energy
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Week 3 – 2 Kinetic Theory of Gases Agenda    Pressure   Temperature   Reading: Chapter 19   New Homework   The quizzes will be in  STSS 220 66 The temperature of an ideal  monatomic gas is related to  the average kinetic energy -  Wikipedia
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7 Kinetic theory of gases Collisions will be elastic. Hard sphere repulsion at short range (0.3 nm spacing). Weak interactions at longer range (> 3 nm spacing). Van der Waals interaction energy for N2 molecules – Virginia University Molecule – molecule interaction energy
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8 Kinetic Theory Where does pressure come from? When molecules collide with the wall, there is an average force. P = F / A Why is the pressure steady? Averaging over a very large number of particles Where does temperature come from? Related to total energy in the gas Sum of the kinetic energies of the molecules mikeblaber.org
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19-2 Pressure and Molecular Motion Given a box containing dilute gas, volume  V , temperature  T . Average velocity in any direction is zero – there is no net  movement of the gas: The brackets indicate  average value. 99
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19-2 RMS Velocity Average velocity is zero. However, actual molecular speeds are high. Therefore use root mean square velocity to characterize speed. We average v2 which is  always positive. 10 10
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19-2 Pressure and Molecular Motion Internal energy  U  comes mostly from the kinetic energies of  the molecules: The average squares of velocities in all three directions are  the same: 11 11
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19-2 Pressure and Molecular Motion Now, relate             to the pressure of the gas:
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