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

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SUMMARY

The number of degrees of freedom for a diatomic gas is 5 when vibrational energy is excluded, but increases to 7 when vibrational energy is included. The discussion highlights that for vibrational motion, the kinetic energy contributes one degree of freedom, while the potential energy contributes another, leading to a total of 6 degrees of freedom for the two atoms. Additionally, the three spatial degrees of freedom and two rotational degrees of freedom complete the total of 7 degrees of freedom for a diatomic gas.

PREREQUISITES
  • Understanding of kinetic and potential energy concepts
  • Familiarity with degrees of freedom in thermodynamics
  • Basic knowledge of diatomic gas behavior
  • Concept of spatial dimensions in physics
NEXT STEPS
  • Research the implications of degrees of freedom on gas behavior in thermodynamics
  • Study the vibrational modes of diatomic molecules
  • Learn about the equipartition theorem in statistical mechanics
  • Explore the differences between ideal gases and real gases regarding energy contributions
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Students of physics, chemists studying gas behavior, and researchers interested in thermodynamic properties of diatomic gases.

zorro
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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?
 
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It only has 1 due to vibration, I can't think of any other.
 
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?
 
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.
 

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