The two specific heat capacities of a gas are measured as `C_(P)=(12.28+0.2)` units and `C_(V)=(3.97+0.3)` units, if the value of gas constant R is `8.31 pm 0` . x units, the vaslue of x is (Relation : `C_(P)-C_(V)=R`)

Answer

To solve the problem, we need to find the value of \( x \) given the specific heat capacities \( C_P \) and \( C_V \) of a gas, along with the gas constant \( R \). The relationship between these quantities is given by the equation:

\[ C_P - C_V = R \]

### Step-by-step Solution:

1. **Identify the values of \( C_P \) and \( C_V \)**:
- Given:
\[ C_P = 12.28 \pm 0.2 \quad \text{units} \]
\[ C_V = 3.97 \pm 0.3 \quad \text{units} \]

2. **Calculate \( C_P - C_V \)**:
- Using the values of \( C_P \) and \( C_V \):
\[ C_P - C_V = 12.28 - 3.97 \]
- Performing the subtraction:
\[ C_P - C_V = 8.31 \quad \text{units} \]

3. **Determine the error in \( R \)**:
- The error in \( R \) is calculated by adding the absolute errors of \( C_P \) and \( C_V \):
\[ \Delta R = \Delta C_P + \Delta C_V \]
- Substituting the errors:
\[ \Delta R = 0.2 + 0.3 = 0.5 \quad \text{units} \]

4. **Express \( R \) with its error**:
- We can express \( R \) as:
\[ R = 8.31 \pm 0.5 \quad \text{units} \]
- This can be written in the form \( 8.31 \pm 0.x \) where \( x = 5 \).

5. **Conclusion**:
- Therefore, the value of \( x \) is:
\[ x = 5 \]

### Final Answer:
The value of \( x \) is \( 5 \).