For a gas, molar specific heat in a process is greater then `C_V` . Which of the following relation is possible?

Options

A. `P^2 V^(1/3)=C`
B. `PV^2 = C`
C. `PV^3 = C`
D. ` P^2 V^2 = C`

Explanation

To solve the problem, we need to analyze the relationship between the molar specific heat in a process (C) and the molar specific heat at constant volume (C_V) for a gas.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We are given that the molar specific heat in a process (C) is greater than the molar specific heat at constant volume (C_V). Mathematically, this can be expressed as:
\[ C > C_V \]

2. **Using the Relation for Molar Specific Heat**:
The molar specific heat (C) can be expressed in terms of C_V and the gas constant (R) as follows:
\[ C = C_V + \frac{R}{1 - x} \]
where \(x\) is a parameter that characterizes the process.

3. **Analyzing the Condition**:
Since we know that \(C > C_V\), we can substitute this into our equation:
\[ C_V + \frac{R}{1 - x} > C_V \]
This simplifies to:
\[ \frac{R}{1 - x} > 0 \]

4. **Determining the Condition on x**:
For the term \(\frac{R}{1 - x}\) to be positive, the denominator must be positive:
\[ 1 - x > 0 \implies x < 1 \]

5. **Conclusion**:
The condition \(x < 1\) indicates that the process is such that the parameter \(x\) must be less than 1. This gives us the possible relation for the molar specific heat in this process.

### Final Answer:
The relation that is possible when the molar specific heat in a process is greater than \(C_V\) is:
\[ x < 1 \]