`C_p`and `C_v` are specific heats at constant pressure and constant volume respectively. It is observed that `C_p - C_v = a` for hydrogen gas
`C_p = C_V = b` for nitrogen gas
The correct relation between a and b is:

Options

A. `a = 28 b`
B. `a = 1/ 14 b`
C. `a = b`
D. `a = 14 b`

Explanation

To solve the problem, we need to analyze the specific heats at constant pressure (`C_p`) and constant volume (`C_v`) for hydrogen and nitrogen gases.

### Step-by-Step Solution:

1. **Understanding the relationship between `C_p` and `C_v`:**
The difference between specific heats at constant pressure and constant volume for any gas is given by the equation:
\[ C_p - C_v = R/M \]
where \( R \) is the universal gas constant and \( M \) is the molar mass of the gas.

2. **For Hydrogen Gas:**
We are given that:
\[ C_p - C_v = a \]
For hydrogen, the molar mass \( M \) is approximately 2 g/mol. Therefore, we can write:
\[ a = \frac{R}{2} \]

3. **For Nitrogen Gas:**
We are also given that:
\[ C_p - C_v = b \]
For nitrogen, the molar mass \( M \) is approximately 28 g/mol. Thus, we can write:
\[ b = \frac{R}{28} \]

4. **Finding the relationship between `a` and `b`:**
We can now relate `a` and `b` using the equations derived:
\[ \frac{a}{b} = \frac{\frac{R}{2}}{\frac{R}{28}} \]
Simplifying this gives:
\[ \frac{a}{b} = \frac{R}{2} \cdot \frac{28}{R} = \frac{28}{2} = 14 \]
Therefore, we can express this as:
\[ a = 14b \]

5. **Conclusion:**
The correct relation between `a` and `b` is:
\[ a = 14b \]

### Final Answer:
The correct relation between `a` and `b` is \( a = 14b \).