Degrees of Freedom of a Diatomic Gas: 5 or 7?

In summary, the number of degrees of freedom for a diatomic gas is 5 if vibrational energy is not considered, but increases to 7 if vibrational energy is included. The independent quantities needed to specify vibrational motion are the kinetic energy and potential energy of vibration. However, since ideal gases do not have potential energy, the total number of degrees of freedom is reduced to 6. This is due to the 1 degree of freedom for vibration and 2 degrees of freedom for rotation. A system of particles can have a maximum of 3N degrees of freedom, and in the case of 2 connected particles, there are 6 degrees of freedom. These include three spatial degrees, 1 vibrational degree of freedom,
  • #1
zorro
1,384
0
The number of degrees of freedom of a diatomic gas is 5 if vibrational energy is not considered
However, if we consider their vibration, total number of degrees of freedom is 7.

What independent quantities do we need to specify for vibrational motion of the pair of atoms? If it is the kinetic energy of vibration about their common centre of mass, then the total no. of degrees of freedom should be 6. What is the other independent quantity?
 
Physics news on Phys.org
  • #2
It only has 1 due to vibration, I can't think of any other.
 
  • #3
I got its answer.
The second one is due to potential energy of vibration (first 1 due to kinetic energy).
But ideal gases don't have any potential energy, then how come there are 2 degrees of freedom?
 
  • #4
A system of particles can have max (?) 3N degrees of freedom where N is the number of particles. In your case 2 connected particles can have 6 degrees of freedom.

Three spatial degrees, where it is in x, y, z space.

1 vibrational DOF like a spring connecting them

2 rotational degrees of freedom.
 
  • #5


The other independent quantity for vibrational motion of a diatomic gas is the potential energy of the bond between the two atoms. This potential energy is dependent on the distance between the atoms and the strength of the bond, and therefore adds another degree of freedom to the system. So, the total number of degrees of freedom for a diatomic gas with vibrational motion is 6, with 3 degrees of freedom for translational motion, 2 for rotational motion, and 1 for vibrational motion.
 

1. What is the concept of degrees of freedom in relation to a diatomic gas?

The concept of degrees of freedom in a diatomic gas refers to the number of independent ways that the gas molecules can move and store energy. In other words, it represents the number of variables needed to fully describe the state of the gas.

2. How many degrees of freedom does a diatomic gas have?

A diatomic gas has a total of 5 degrees of freedom. This includes the translational, rotational, and vibrational motions of the two atoms in the molecule.

3. Why is it sometimes stated that a diatomic gas has 7 degrees of freedom?

This statement is based on the assumption that the diatomic molecule can also undergo electronic transitions, which would add 2 additional degrees of freedom. However, in most cases, these transitions are not significant and can be ignored, making the total number of degrees of freedom 5.

4. How does the number of degrees of freedom affect the energy of a diatomic gas?

The energy of a diatomic gas is directly related to the number of degrees of freedom. In general, the more degrees of freedom a gas has, the more energy it can store and the higher its specific heat capacity will be.

5. What is the significance of degrees of freedom in thermodynamics?

In thermodynamics, degrees of freedom are important for understanding the behavior of gases and how they interact with their surroundings. They are used to calculate the internal energy, specific heat capacity, and other thermodynamic properties of a gas.

Similar threads

  • Advanced Physics Homework Help
Replies
4
Views
834
  • Introductory Physics Homework Help
Replies
11
Views
967
  • Other Physics Topics
Replies
4
Views
15K
  • Introductory Physics Homework Help
Replies
8
Views
3K
Replies
2
Views
967
  • Atomic and Condensed Matter
Replies
3
Views
1K
  • Advanced Physics Homework Help
Replies
23
Views
5K
  • Other Physics Topics
Replies
6
Views
3K
Replies
17
Views
2K
  • Other Physics Topics
Replies
6
Views
2K
Back
Top