The average value of rotational kinetic energy of one mole of oxygen gas at temperature T will be

Options

A. RT
B. `3/2` RT
C. `5/2` RT
D. `1/2` RT

Answer

To find the average value of rotational kinetic energy of one mole of oxygen gas at temperature T, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Type of Gas**:
Oxygen gas (O₂) is a diatomic molecule.

2. **Determine Degrees of Freedom**:
For a diatomic gas, the degrees of freedom (f) can be categorized as:
- Translational degrees of freedom: 3 (movement in x, y, z directions)
- Rotational degrees of freedom: 2 (rotation about two axes)
- Vibrational degrees of freedom: Typically not considered at room temperature for this calculation.

Thus, the total degrees of freedom for a diatomic gas like oxygen is 5 (3 translational + 2 rotational).

3. **Use the Formula for Average Kinetic Energy**:
The average kinetic energy (KE) per degree of freedom is given by:
\[ KE = \frac{f}{2} RT \]
where R is the universal gas constant and T is the absolute temperature.

4. **Substitute the Degrees of Freedom**:
Since we are interested in the rotational kinetic energy, we will only consider the rotational degrees of freedom (f = 2):
\[ KE_{rotational} = \frac{2}{2} RT = RT \]

5. **Conclusion**:
Therefore, the average value of the rotational kinetic energy of one mole of oxygen gas at temperature T is:
\[ KE_{rotational} = RT \]

### Final Answer:
The average value of rotational kinetic energy of one mole of oxygen gas at temperature T is \( RT \).