# Kinetic Theory of Gases and Equipartition Theorem - PowerPoint PPT Presentation

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## Kinetic Theory of Gases and Equipartition Theorem

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### Kinetic Theory of Gases and Equipartition Theorem Results of Kinetic Theory KE of individual particles is related to the temperature of the gas: mv2 = 3/2 kT Where ... – PowerPoint PPT presentation

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Title: Kinetic Theory of Gases and Equipartition Theorem

1
Kinetic Theory of Gases and Equipartition Theorem
2
Results of Kinetic Theory
• KE of individual particles is related to the
temperature of the gas
• ½ mv2 3/2 kT
• Where v is the average velocity.

3
Boltzmann Distribution
• Demonstrated that there is a wide range of speeds
that varies with temperature.

4
Equipartition of Energy
• The Kinetic Theory result tells us that the
average translational KE is proportional to the
temperature.
• Types of allowed motion are referred to as
Degrees of Freedom (DOF)
• Linear motion in three directions (x,y,z) is
three DOF.

5
Equipartition of Energy
• Each degree of translational freedom takes ½ kT.
• KEx KEyKEz ½ kT ½ kT ½ kT
• KEtotal 3/2 kT
• This is true for single point masses that possess
no structure.

6
Equipartition of Energy
• For molecules, i.e. multi-atom particles, there

7
Equipartition of Energy
• Each new DOF requires ½ kT of energy.
• Each new DOF contributes ½ kT to the total
internal energy of the gas. This is the
Equipartition Theorem.

8
Internal Energy, U
• The internal energy of a gas is the sum of all
the kinetic and potential energies.
• U KE PE.
• For an ideal gas we allow no PE of interaction,
so U is comprised solely of the various type of
kinetic energies, i.e. translational, rotational
and vibrational.

9
Internal Energy of Di-Atom
• Three translational DOF 2 rotational DOF 5
DOF.
• Each DOF contributes ½ kt, so the internal energy
of a diatomic gas is,
• U 5/2 NkT,
• For a gas of N molecules.