The difference between `C_(p)` and `C_(v)` for a diatomic gas is nR. The value of n is

Explanation

To find the value of \( n \) in the equation \( C_p - C_v = nR \) for a diatomic gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- \( C_p \) is the specific heat at constant pressure.
- \( C_v \) is the specific heat at constant volume.

2. **Use the Relationship for Ideal Gases**:
- For any ideal gas, the relationship between \( C_p \) and \( C_v \) is given by:
\[ C_p = C_v + R \]

3. **Specific Values for a Diatomic Gas**:
- For a diatomic gas, the specific heats are:
\[ C_p = \frac{7}{2}R \]
\[ C_v = \frac{5}{2}R \]

4. **Calculate \( C_p - C_v \)**:
- Now, substituting the values of \( C_p \) and \( C_v \):
\[ C_p - C_v = \frac{7}{2}R - \frac{5}{2}R \]

5. **Simplify the Expression**:
- Simplifying the above expression:
\[ C_p - C_v = \left(\frac{7}{2} - \frac{5}{2}\right)R = \frac{2}{2}R = R \]

6. **Equate to \( nR \)**:
- According to the problem statement, we have:
\[ C_p - C_v = nR \]
- From our calculation, we found that:
\[ C_p - C_v = R \]
- Therefore, we can equate:
\[ nR = R \]

7. **Solve for \( n \)**:
- Dividing both sides by \( R \) (assuming \( R \neq 0 \)):
\[ n = 1 \]

### Final Answer:
The value of \( n \) is \( 1 \).

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