MasteringPhysics18 - MasteringPhysics Assignment Print View...

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MasteringPhysics: Assignment Print View .. 1 of 11 12/19/2007 1:04 PM [ Print View ] PHCC 141: Physics for Scientists and Engineers I - Fall 2007 18. Thermal Properties of Matter Due at 11:59pm on Monday, November 26, 2007 Hide Grading Details Number of answer attempts per question is: 5 You gain credit for: correctly answering a question in a Part, or correctly answering a question in a Hint. You lose credit for: exhausting all attempts or requesting the answer to a question in a Part or Hint, or incorrectly answering a question in a Part. Late submissions: reduce your score by 100% over each day late. Hints are helpful clues or simpler questions that guide you to the answer. Hints are not available for all questions. There is no penalty for leaving questions in Hints unanswered. Grading of Incorrect Answers For Multiple-Choice or True/False questions, you lose 100% / ( # of options - 1 ) credit per incorrect answer. For any other question, you lose 3% credit per incorrect answer. Equipartition Theorem and Microscopic Motion Learning Goal: To understand the Equipartition Theorem and its implications for the mechanical motion of small objects. In statistical mechanics, heat is the random motion of the microscopic world. The average kinetic or potential energy of each degree of freedom of the microscopic world therefore depends on the temperature. If heat is added, molecules increase their translational and rotational speeds, and the atoms constituting the molecules vibrate with larger amplitude about their equilibrium positions. It is a fact of nature that the energy of each degree of freedom is determined solely by the temperature . The Equipartition Theorem states this quantitatively: The average energy associated with each degree of freedom in a system at absolute temperature is , where is Boltzmann's constant. The average energy of the i th degree of freedom is , where the angle brackets represent "average" or "mean" values of the enclosed variable. A "degree of freedom" corresponds to any dynamical variable that appears quadratically in the energy. For instance, is the kinetic energy of a gas particle of mass with velocity component along the x axis. The Equipartition Theorem follows from the fundamental postulate of statistical mechanics--that every energetically accessible quantum state of a system has equal probability of being populated, which in turn leads to the Boltzmann distribution for a system in thermal equilibrium. From the standpoint of an introductory physics course, equipartition is best regarded as a principle that is justified by observation. In this problem we first investigate the particle model of an ideal gas. An ideal gas has no interactions among its particles, and so its internal energy is entirely "random" kinetic energy. If we consider the gas as a system, its internal energy is analogous to the energy stored in a spring. If one end of the gas container is fitted with a sliding piston, the pressure of the gas on the piston can
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This note was uploaded on 10/28/2008 for the course PH 141 taught by Professor Toki during the Fall '08 term at Colorado State.

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MasteringPhysics18 - MasteringPhysics Assignment Print View...

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