Molar specific heat of a monatomic gas at constant pressure is

Options

A. 5/2 R
B. 3/2 RT
C. 7/2 R
D. R

Explanation

To find the molar specific heat of a monatomic gas at constant pressure (Cp), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Degrees of Freedom**:
- For a monatomic gas, the degrees of freedom (f) is 3. This is because monatomic gases can only translate in three dimensions (x, y, z) and do not have rotational or vibrational degrees of freedom.

2. **Use the Relation Between Cp and Cv**:
- The relationship between the molar specific heats at constant pressure (Cp) and constant volume (Cv) is given by:
\[ Cp - Cv = R \]
where R is the universal gas constant.

3. **Determine Cv for a Monatomic Gas**:
- The molar specific heat at constant volume (Cv) for a monatomic gas can be calculated using the formula:
\[ Cv = \frac{f}{2} R \]
- Since f = 3 for a monatomic gas:
\[ Cv = \frac{3}{2} R \]

4. **Calculate Cp**:
- Now, substituting Cv into the equation for Cp:
\[ Cp = Cv + R \]
- Substituting the value of Cv:
\[ Cp = \frac{3}{2} R + R \]
- This simplifies to:
\[ Cp = \frac{3}{2} R + \frac{2}{2} R = \frac{5}{2} R \]

5. **Final Result**:
- Therefore, the molar specific heat of a monatomic gas at constant pressure (Cp) is:
\[ Cp = \frac{5}{2} R \]

### Summary:
The molar specific heat of a monatomic gas at constant pressure is \( \frac{5}{2} R \).