ch21 - The Big Ideas-Chapter 21(Serway and Beichner Physics...

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The Big Ideas—Chapter 21 (Serway and Beichner, Physics for Scientists and Engineers, 5 th Edition) AJM:2/17/01 1 Section 1 The ideal gas law is the natural result of a very simple model of a gas (in which molecules behave like particles that undergo elastic contact collisions with walls and other molecules) and an interpretation of temperature as a measure of the average energy per molecule. In this model the pressure arises from the average force of the collisions between the molecules and the walls and is directly associated with the density and the average translational kinetic energy of the molecules. The ideal gas law then reveals temperature as a pure function of the average translational kinetic energy. With far more generality than is implied by the derivation of this simple model, the “equipartition theorem” says that, for a system in thermal equilibrium, every possible way in which a molecule can store energy (each so-called “degree of freedom”) will on average store an energy determined solely by the temperature. P simple model = 2 3 N V 1 2 mv 2 ( 29 T ideal gas = 2 3 k B 1 2 mv 2 ( 29 1 2 mv 2 = 3 2 k B T Energy per degreee of freedom = 1 2 k B T Section 2 The equipartition theorem allows us easily to determine the internal energy of an ideal gas since the value depends only on how many molecules there are and on how many ways each molecules can translate, rotate and/or vibrate.
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