The value of `C_(V)` for monatomic gas is `(3)/(2)R`, then `C_(P)` will be

Options

A. `(1)/(2)R`
B. `(7)/(2)R`
C. `(5)/(2)R`
D. `(3)/(2)R`

Answer

To find the value of \( C_P \) for a monatomic gas given that \( C_V = \frac{3}{2}R \), we can use Mayer's relation, which states:

\[ C_P - C_V = R \]

### Step-by-Step Solution:

1. **Identify the given value of \( C_V \)**:
- We know that \( C_V = \frac{3}{2}R \).

2. **Apply Mayer's relation**:
- According to Mayer's relation, we have:
\[ C_P = C_V + R \]

3. **Substitute the value of \( C_V \)**:
- Substitute \( C_V = \frac{3}{2}R \) into the equation:
\[ C_P = \frac{3}{2}R + R \]

4. **Convert \( R \) into a fraction with a common denominator**:
- We can express \( R \) as \( \frac{2}{2}R \) to have a common denominator:
\[ C_P = \frac{3}{2}R + \frac{2}{2}R \]

5. **Combine the fractions**:
- Now, we can combine the two fractions:
\[ C_P = \frac{3 + 2}{2}R = \frac{5}{2}R \]

6. **Final result**:
- Thus, the value of \( C_P \) is:
\[ C_P = \frac{5}{2}R \]

### Conclusion:
The correct answer is \( C_P = \frac{5}{2}R \).