If `C_(p) and C_(v)` denoted the specific heats of unit mass of nitrogen at constant pressure and volume respectively, then

Options

A. `C_(p)=C_(v)=( R)/(28)`
B. `C_(p)-C_(v)=(R )/(7)`
C. `C_(p)-C_(v)=(R )/(14)`
D. `C_(p)-C_(v)=R`

Explanation

To find the relationship between the specific heats at constant pressure (C_p) and constant volume (C_v) for nitrogen, we can follow these steps:

### Step 1: Understand the relationship between C_p and C_v
The relationship between the specific heats at constant pressure and volume for an ideal gas is given by the equation:
\[ C_p - C_v = R \]
where \( R \) is the universal gas constant.

### Step 2: Adjust the equation for unit mass
The equation \( C_p - C_v = R \) is typically used for one mole of gas. For a unit mass of gas, we need to express \( R \) in terms of the molecular mass \( M \) of the gas. The relationship becomes:
\[ C_p - C_v = \frac{R}{M} \]
where \( M \) is the molecular mass of the gas.

### Step 3: Substitute the molecular mass of nitrogen
The molecular mass of nitrogen (N₂) is approximately 28 g/mol. Therefore, we can substitute \( M = 28 \) into the equation:
\[ C_p - C_v = \frac{R}{28} \]

### Step 4: Conclusion
Thus, the final relationship between the specific heats for unit mass of nitrogen is:
\[ C_p - C_v = \frac{R}{28} \]

### Final Answer
The relationship is:
\[ C_p - C_v = \frac{R}{28} \]

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