The Equipartition Theorem 
The Equipartition Theorem
by UC Irvine
Video Lecture 5 of 27
Copyright Information: Penner, Reginald Thermodynamics and Chemical Dynamics 131C (UCI OpenCourseWare: University of California, Irvine), [January 28, 2015]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (
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Date Added: January 28, 2015

Lecture Description

Recorded on April 11, 2012.

Slide Information:
00:21 - Announcements
02:34 - Diagram: in real molecules, the situation is considerably more complex than the Harmonic Oscillator
03:20 - We have a very high density of translational states that are not, in reality...
03:36 - Diagram: these translational states are nested within rotational states
03:58 - Diagrams (many rotational states)
04:23 - ...we can treat each of these energetic manifolds...
05:45 - What's in this Lecture
05:51 - Your book mainly focuses attention on...
07:27 - Graph 5-13: Here is what happens to Cv as a function of T for a diatomic molecule:
10:04 - Graph 5-13 These are the rotation temperature...
11:08 - Graph 5-13 Here is what happens to Cv as a function of T...
11:37 - The Equipartition Theorum
12:10 - The Equipartition Theorum (with diagram)
13:17 - consider the classical Hamiltonian for a I D harmonic oscillator:
14:16 - now you'll recall that the heat capacity...
15:03 - Example: Formula
15:50 - Graph
16:13 - ...this is also the heat capacity for all monoatomic gases...
18:29 - For a linear molecule...
19:41 - Graph (Translation + Rotation)
20:26 - For a nonlinear molecule...
20:54 - What about for higher temperatures?
22:08 - so following through with the predictions of the equipartition theorem...
23:05 - so for a diatomic molecule...
24:24 - Example: Use the equipartition theorem to estimate...
31:18 - Example: Use the equipartition theorum to estimate... (Part B)
34:36 - Example: (Chart) "Use the equipartition theorum to estimate... (Part C)
38:55 - Calculate Each Term
39:18 - We'll Start with Translation...
39:40 - The translational energy of a classical gas molecule is:
40:15 - ...And a quantum mechanical gas has energies given by the particle-in-a-box model.
40:23 - we'll concentrate attention now on ideal monoatomic gases...
41:27 - consider first a monoatomic gas in one dimension.
43:59 - these energies are very closely spaced. Consider, for example, an argon atom in a box...
45:25 - Log Scale
45:52 - ...if these states are quasi-continuous, we can rewrite this summation...
46:54 - so after integration we have...
47:05 - Example "Calculate..."
48:26 - What would...three dimensional cube?
49:36 - terms we calculate its transitional energy.
50:03 - ...and this yields a very simple expression

Course Index

Course Description

In Chemistry 131C, students will study how to calculate macroscopic chemical properties of systems. This course will build on the microscopic understanding (Chemical Physics) to reinforce and expand your understanding of the basic thermo-chemistry concepts from General Chemistry (Physical Chemistry.) We then go on to study how chemical reaction rates are measured and calculated from molecular properties. Topics covered include: Energy, entropy, and the thermodynamic potentials; Chemical equilibrium; and Chemical kinetics.

Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine


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