If the molar specific heat capacity at constant volume of an ideal gas is `C_(v) = 3/2 R`, then what is the corresponding molar specific heat capacity of the ideal gas at constant pressure ?

Options

A. `1/2 R`
B. `5/2 R`
C. `7/2 R`
D. `9/2 R`

Explanation

To find the molar specific heat capacity at constant pressure \( C_p \) for an ideal gas when the molar specific heat capacity at constant volume \( C_v \) is given as \( \frac{3}{2} R \), we can use the relationship between \( C_p \) and \( C_v \).

### Step-by-Step Solution:

1. **Recall the relationship between \( C_p \) and \( C_v \)**:
The relationship for an ideal gas is given by the equation:
\[ C_p - C_v = R \]
where \( R \) is the universal gas constant.

2. **Substitute the value of \( C_v \)**:
From the problem, we know that:
\[ C_v = \frac{3}{2} R \]
Now, substitute this value into the equation:
\[ C_p - \frac{3}{2} R = R \]

3. **Rearrange the equation to solve for \( C_p \)**:
To find \( C_p \), we can rearrange the equation:
\[ C_p = R + \frac{3}{2} R \]

4. **Combine the terms**:
Now, combine the terms on the right side:
\[ C_p = \frac{2}{2} R + \frac{3}{2} R = \frac{5}{2} R \]

5. **Final answer**:
Thus, the molar specific heat capacity at constant pressure \( C_p \) is:
\[ C_p = \frac{5}{2} R \]

### Conclusion:
The corresponding molar specific heat capacity of the ideal gas at constant pressure is \( \frac{5}{2} R \).