For nitrogen `C_(p)-C_(V)=x` and for argon `C_(P)-C_(V)`=Y. The relation between x and y is given by a) x = y b) x = 7y c) y = 7x d) x = 1/2 y

Options

A. x=y
B. x=7y
C. y=7x
D. `x=(1)/(2)y`

Explanation

To solve the problem, we need to find the relationship between \( x \) and \( y \) given the equations for specific heat capacities of nitrogen and argon.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- For any ideal gas, the difference between the specific heat at constant pressure (\( C_p \)) and the specific heat at constant volume (\( C_v \)) is given by the equation:
\[ C_p - C_v = R \]
where \( R \) is the universal gas constant.

2. **Apply the Relation to Nitrogen**:
- For nitrogen (\( N_2 \)), we have:
\[ C_p - C_v = x \]
- According to the general relation, we can also express this as:
\[ x = R \]

3. **Apply the Relation to Argon**:
- For argon, we similarly have:
\[ C_p - C_v = y \]
- Again, using the general relation, we can express this as:
\[ y = R \]

4. **Establish the Relationship**:
- Since both \( x \) and \( y \) are equal to \( R \):
\[ x = R \quad \text{and} \quad y = R \]
- Therefore, we can conclude:
\[ x = y \]

5. **Select the Correct Option**:
- The relationship we derived is \( x = y \).
- Thus, the correct answer is option (a) \( x = y \).

### Final Answer:
The relationship between \( x \) and \( y \) is \( x = y \) (Option a).