What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules?

Options

A. `(3)/(2)R`
B. `(5)/(2)R`
C. R
D. `3R`

Explanation

To find the molar specific heat at constant volume (\(C_V\)) of an ideal gas consisting of rigid diatomic molecules, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Degrees of Freedom**:
- For a diatomic molecule, if it were not rigid, it would have 7 degrees of freedom: 3 translational, 2 rotational, and 2 vibrational.
- However, since we are considering rigid diatomic molecules, the vibrational degrees of freedom are not considered. Therefore, the total degrees of freedom (\(f\)) for rigid diatomic molecules is:
\[ f = 3 \text{ (translational)} + 2 \text{ (rotational)} = 5 \]

2. **Using the Formula for Molar Specific Heat at Constant Volume**:
- The molar specific heat at constant volume (\(C_V\)) is related to the degrees of freedom by the formula:
\[ C_V = \frac{f \cdot R}{2} \]
- Here, \(R\) is the universal gas constant.

3. **Substituting the Degrees of Freedom**:
- Now, substituting \(f = 5\) into the equation:
\[ C_V = \frac{5 \cdot R}{2} \]

4. **Final Expression**:
- Therefore, the molar specific heat at constant volume for an ideal gas consisting of rigid diatomic molecules is:
\[ C_V = \frac{5R}{2} \]

### Conclusion:
The molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules is \(\frac{5R}{2}\).

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