The molar specific heat at constant pressure of an ideal gas is `(7//2 R)`. The ratio of specific heat at constant pressure to that at constant volume is

Options

A. `7/5`
B. `8/7`
C. `5/7`
D. `9/7`

Explanation

To solve the problem, we need to find the ratio of the specific heat at constant pressure (Cp) to the specific heat at constant volume (Cv) for an ideal gas. We are given that the molar specific heat at constant pressure (Cp) is \( \frac{7}{2} R \).

### Step-by-Step Solution:

1. **Identify the given values**:
- Molar specific heat at constant pressure, \( C_p = \frac{7}{2} R \).

2. **Use the relationship between Cp and Cv**:
- For an ideal gas, the relationship between the specific heats is given by:
\[ C_p - C_v = R \]
- We can rearrange this equation to find \( C_v \):
\[ C_v = C_p - R \]

3. **Substitute the value of Cp**:
- Substitute \( C_p = \frac{7}{2} R \) into the equation:
\[ C_v = \frac{7}{2} R - R \]
- To simplify, convert \( R \) to a fraction with a common denominator:
\[ C_v = \frac{7}{2} R - \frac{2}{2} R = \frac{5}{2} R \]

4. **Calculate the ratio \( \frac{C_p}{C_v} \)**:
- Now we need to find the ratio of \( C_p \) to \( C_v \):
\[ \frac{C_p}{C_v} = \frac{\frac{7}{2} R}{\frac{5}{2} R} \]
- The \( R \) and \( \frac{2}{2} \) cancel out:
\[ \frac{C_p}{C_v} = \frac{7}{5} \]

5. **Final answer**:
- The ratio of specific heat at constant pressure to that at constant volume is:
\[ \frac{C_p}{C_v} = \frac{7}{5} \]

### Conclusion:
The answer to the question is \( \frac{7}{5} \).

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