The molar specific heat of a gas as given from the kinetic theory is `(5)/(2) R`. If it is not specified whether it is `C_(p) or C_(upsilon)` one could conclude that the molecules of the gas

Options

A. are definitely monoatomic
B. are definitely regid diatomic
C. are definited non - rigid diatmic
D. can be monoatomic or rigid diatomic

Answer

To solve the problem, we need to determine the type of gas based on its molar specific heat given as \( \frac{5}{2} R \). We will analyze the specific heats for monoatomic and diatomic gases.

### Step-by-Step Solution:

1. **Understanding Molar Specific Heat**:
The molar specific heat at constant volume (\( C_v \)) and at constant pressure (\( C_p \)) are related by the equation:
\[ C_p = C_v + R \]
where \( R \) is the universal gas constant.

2. **Molar Specific Heat for Monoatomic Gases**:
For a monoatomic gas, the molar specific heat at constant volume is given by:
\[ C_v = \frac{3}{2} R \]
Using the relation for \( C_p \):
\[ C_p = C_v + R = \frac{3}{2} R + R = \frac{5}{2} R \]
Thus, for a monoatomic gas, both \( C_p \) and \( C_v \) can be \( \frac{5}{2} R \) (specifically \( C_p \)).

3. **Molar Specific Heat for Diatomic Gases**:
For a diatomic gas, the molar specific heat at constant volume is given by:
\[ C_v = \frac{5}{2} R \]
Again, using the relation for \( C_p \):
\[ C_p = C_v + R = \frac{5}{2} R + R = \frac{7}{2} R \]
Thus, for a diatomic gas, \( C_v \) is \( \frac{5}{2} R \) and \( C_p \) is \( \frac{7}{2} R \).

4. **Conclusion**:
Since the molar specific heat provided in the question is \( \frac{5}{2} R \) and it is not specified whether it is \( C_p \) or \( C_v \), we can conclude that the gas could either be:
- A monoatomic gas (where \( C_p = \frac{5}{2} R \))
- A diatomic gas (where \( C_v = \frac{5}{2} R \))

Therefore, the molecules of the gas can be either monoatomic or rigid diatomic.

### Final Answer:
The molecules of the gas can be either monoatomic or rigid diatomic.