The ratio of the molar heat capacities of a diatomic gas at constant pressure to that at constant volume is

Options

A. `7/5`
B. `3/2`
C. `3/5`
D. `5/2`

Explanation

To find the ratio of the molar heat capacities of a diatomic gas at constant pressure (C_P) to that at constant volume (C_V), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Molar Heat Capacities for a Diatomic Gas**:
- For a diatomic gas, the molar heat capacity at constant pressure (C_P) is given by:
\[ C_P = \frac{7}{2} R \]
- The molar heat capacity at constant volume (C_V) is given by:
\[ C_V = \frac{5}{2} R \]

2. **Write the Ratio of C_P to C_V**:
- We need to find the ratio \( \frac{C_P}{C_V} \):
\[ \frac{C_P}{C_V} = \frac{\frac{7}{2} R}{\frac{5}{2} R} \]

3. **Simplify the Ratio**:
- The \( R \) terms in the numerator and denominator cancel out:
\[ \frac{C_P}{C_V} = \frac{7/2}{5/2} = \frac{7}{5} \]

4. **Final Answer**:
- Therefore, the ratio of the molar heat capacities of a diatomic gas at constant pressure to that at constant volume is:
\[ \frac{C_P}{C_V} = \frac{7}{5} \]