A lomecole of a gas has six degrees of freedom. Then the molar specific heat of the gas at constant volume is

Options

A. `R/2`
B. R
C. `(3R)/(2)`
D. 3R

Explanation

To solve the problem, we need to find the molar specific heat of a gas at constant volume (Cv) given that the gas has six degrees of freedom.

### Step-by-Step Solution:

1. **Understanding Degrees of Freedom**:
- Degrees of freedom (F) refer to the number of independent ways in which a molecule can store energy. For a gas molecule, the degrees of freedom can be translational, rotational, and vibrational.

2. **Using the Formula for Molar Specific Heat**:
- The molar specific heat at constant volume (Cv) is related to the degrees of freedom by the formula:
\[ C_v = \frac{F}{2} R \]
where \( R \) is the universal gas constant.

3. **Substituting the Given Degrees of Freedom**:
- In this problem, we are given that the gas has 6 degrees of freedom (F = 6). We can substitute this value into the formula:
\[ C_v = \frac{6}{2} R \]

4. **Calculating Cv**:
- Simplifying the equation:
\[ C_v = 3R \]

5. **Conclusion**:
- Therefore, the molar specific heat of the gas at constant volume is \( 3R \).

### Final Answer:
The molar specific heat of the gas at constant volume is \( 3R \).