Total degrees of freedom of one molecule of a diatomic gas at normal temperature is

Options

A. 2
B. 5
C. 6
D. 8

Answer

To find the total degrees of freedom of one molecule of a diatomic gas at normal temperature, we can analyze the contributions from translational, rotational, and vibrational motions.

### Step-by-Step Solution:

1. **Identify Translational Degrees of Freedom**:
- A diatomic gas molecule can move in three-dimensional space. This means it can translate along the x, y, and z axes.
- Therefore, the translational degrees of freedom (DOF) = 3.

2. **Identify Rotational Degrees of Freedom**:
- A diatomic molecule can rotate about two axes that are perpendicular to the line connecting the two atoms.
- It cannot rotate about the axis that passes through the two atoms because the moment of inertia about that axis is zero.
- Therefore, the rotational degrees of freedom (DOF) = 2.

3. **Identify Vibrational Degrees of Freedom**:
- At normal temperature, the vibrational modes of diatomic gases are not excited. Thus, we do not consider vibrational degrees of freedom in this case.
- Therefore, the vibrational degrees of freedom (DOF) = 0.

4. **Calculate Total Degrees of Freedom**:
- Total degrees of freedom = Translational DOF + Rotational DOF + Vibrational DOF
- Total degrees of freedom = 3 (translational) + 2 (rotational) + 0 (vibrational) = 5.

### Final Answer:
The total degrees of freedom of one molecule of a diatomic gas at normal temperature is **5**.

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