For certain process the molar heat capacity of an ideal gas is found to be `(C_v+R/2)` , where `C_v` is the molar heat capacity of the same gas at constant volume. For the given process, it can be concluded that

Options

A. PV=constant
B. `P/V` = constant
C. `V^2/P` = constant
D. None of these

Answer

To solve the problem, we need to analyze the given molar heat capacity of an ideal gas during a certain process, which is given as \( C = C_v + \frac{R}{2} \). Here, \( C_v \) is the molar heat capacity at constant volume and \( R \) is the universal gas constant.

### Step-by-Step Solution:

1. **Identify the given heat capacity equation**:
\[ C = C_v + \frac{R}{2} \]

2. **Recall the relationship for polytropic processes**:
For a polytropic process, the molar heat capacity \( C \) can be expressed as:
\[ C = C_v + \frac{R}{1 - n} \]
where \( n \) is the polytropic index.

3. **Set the two expressions for \( C \) equal to each other**:
\[ C_v + \frac{R}{2} = C_v + \frac{R}{1 - n} \]

4. **Cancel \( C_v \) from both sides**:
\[ \frac{R}{2} = \frac{R}{1 - n} \]

5. **Cross-multiply to eliminate the fractions**:
\[ R(1 - n) = 2R \]

6. **Divide both sides by \( R \) (assuming \( R \neq 0 \))**:
\[ 1 - n = 2 \]

7. **Solve for \( n \)**:
\[ -n = 2 - 1 \implies -n = 1 \implies n = -1 \]

8. **Interpret the value of \( n \)**:
The value \( n = -1 \) indicates that the process follows the equation:
\[ PV^{-1} = \text{constant} \]
or equivalently,
\[ \frac{P}{V} = \text{constant} \]

### Conclusion:
Thus, the process can be concluded as a special case of a polytropic process where \( n = -1 \).