sy24_nov26_07hc - The micro-macro connection Kinetic theory...

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1 The micro-macro connection Kinetic theory connects the micro- and macroscopic aspects of systems. It relates the macroscopic properties of a system to the motion and collisions of its atoms and molecules. Average p and T. What we call temperature T is a direct measure of the average translational kinetic energy What we call pressure p is a direct measure of the number density of molecules, and how fast they are moving ( v rms ) v rms = v 2 ( ) avg = 3 k B T m p = 2 3 N V ε avg T = 2 3 k B avg The average kinetic energy of the molecules of an ideal gas at 10°C has the value K 10 . At what temperature T 1 (in degrees Celsius) will the average kinetic energy of the same gas be twice this value, 2K 10 ? T 1 = 20°C T 1 = 293°C T 1 = 100°C The molecules in an ideal gas at 10°C have a root-mean-square (rms) speed v rms . At what temperature T 2 (in degrees Celsius) will the molecules have twice the rms speed, 2v rms ? T 2 = 859°C T 2 = 20°C T 2 = 786°C Kinetic energy of a gas
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2 Degrees of freedom , or modes of energy storage into the system, can be: • translational for a monoatomic gas (translation along x, y, z axes, energy stored is only kinetic) • rotational for a diatomic gas (rotation about x, y, z axes, energy stored is only kinetic) • vibrational for a diatomic gas (two atoms joined by a spring-like molecular bond vibrate back and forth, both potential and kinetic energy are stored in this vibration) degrees of freedom or “modes”
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This note was uploaded on 10/30/2011 for the course PHYS 207 taught by Professor Winnokur during the Spring '06 term at University of Wisconsin.

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sy24_nov26_07hc - The micro-macro connection Kinetic theory...

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