Calculating Degrees of Freedom

To calculate the degrees of freedom for a system of particles:

1. For N particles in 3D space: Start with 3N (3 coordinates per particle).
2. Subtract any constraints (e.g., fixed distances between particles).
3. For a rigid body: 6 degrees of freedom (3 for position, 3 for orientation).

Example: For a diatomic gas molecule:
- 2 atoms: 2 × 3 = 6 degrees of freedom
- Constraint (fixed bond length): -1
- Total: 5 degrees of freedom (3 translational, 2 rotational)

Understanding degrees of freedom is crucial for analyzing complex systems in thermodynamics and statistical mechanics.