The energy associated with each degree of freedom of a molecule

Options

A. 1/2RT
B. 1/2 KT
C. 3/2 RT
D. 3/2KT

Explanation

To solve the question regarding the energy associated with each degree of freedom of a molecule, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Degrees of Freedom**:
- Degrees of freedom refer to the independent ways in which a molecule can move. For a gas molecule, these typically include translational, rotational, and vibrational motions.
- For a monoatomic gas, there are 3 translational degrees of freedom.
- For a diatomic gas, there are 3 translational and 2 rotational degrees of freedom, making a total of 5 degrees of freedom.

2. **Equipartition of Energy**:
- The principle of equipartition of energy states that each degree of freedom contributes equally to the total energy of the system.
- According to this principle, the energy associated with each degree of freedom is given by \( \frac{1}{2} kT \), where \( k \) is the Boltzmann constant and \( T \) is the absolute temperature.

3. **Calculating Energy for Different Gases**:
- For a monoatomic gas (3 degrees of freedom):
\[ \text{Total energy} = \frac{3}{2} kT \]
- For a diatomic gas (5 degrees of freedom):
\[ \text{Total energy} = \frac{5}{2} kT \]

4. **Conclusion**:
- The energy associated with each degree of freedom for any gas molecule is \( \frac{1}{2} kT \).

### Final Answer:
The energy associated with each degree of freedom of a molecule is \( \frac{1}{2} kT \).

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