Equipartition of Energy

Sunday, 6 May 2018

7:23 PM

Equipartition - each direction of the motion of a molecule stores on average the same amount of energy

 

(for each particle)

 

 

 

 

Degrees of Freedom

Every type of molecule has a certain number of degrees of freedom, expressed as .

This number represents the independent ways in which the molecule can store energy.

 

Each degree of freedom allows the molecule to store  energy.

 

Monatomic (1 atom)

  • Can move in the x, y, z direction - can have KE in each of these directions (translational)
  • Can rotate and have KE but very little as  - mass is concentrated in the nucleus (m)

Therefore: 3 degrees of freedom, and

 

Diatomic Molecules (2 atoms)

  • Translational motion (x, y, z)  3 degrees of freedom
  • Rotational motion around 2 axes  2 degrees of freedom
  • Vibrational motion when   possible extra 1 degree

Therefore 5/6 degrees of freedom, and

 

Polyatomic Molecules (many atoms)

  • Translational motion (x, y, z)  3 degrees of freedom
  • Classically can rotate about 3 axes
  • Up to 15 degrees of freedom

 

Total Energy of a Gas

 

ie in a monatomic gas of N particles:

 

 

Created with Microsoft OneNote 2016.