Degree of freedom

Definition

A degree of freedom in physics describes an independent physical parameter in the formal description of a system. It often refers to the number of independent ways in which the molecules of a gas can move or store energy.

5 Must Know Facts For Your Next Test

1. Degrees of freedom determine how energy is distributed among the different possible modes of motion, such as translational, rotational, and vibrational.
2. For a monatomic gas, there are three translational degrees of freedom corresponding to movement along the x, y, and z axes.
3. Diatomic and polyatomic gases have additional rotational and sometimes vibrational degrees of freedom.
4. The equipartition theorem states that each degree of freedom contributes $\frac{1}{2} k_B T$ to the total internal energy, where $k_B$ is Boltzmann's constant and $T$ is temperature.
5. Heat capacity at constant volume ($C_V$) for an ideal gas can be derived using degrees of freedom: $C_V = \frac{f}{2} R$, where $f$ is the number of degrees of freedom and $R$ is the universal gas constant.

Review Questions

• How many translational degrees of freedom does a monatomic gas have?
• According to the equipartition theorem, how much energy does each degree of freedom contribute?
• Why do diatomic gases have more degrees of freedom than monatomic gases?

Related terms

Equipartition Theorem:

A principle stating that energy is equally distributed among all available degrees of freedom.

Translational Motion: Movement along one or more of three possible axes (x, y, z) in space.

$C_V$ (Heat Capacity at Constant Volume): The amount of heat needed to raise the temperature of a substance by one degree Celsius at constant volume.