1. For an ideal gas, the relation between molar specific heats is $C_{p,m} - C_{v,m} = R$ where $R$ is the universal gas constant.

2. But in the question, $C_p$ and $C_v$ are specific heats per unit mass (not per mole).

3. For specific heats per unit mass, the corresponding relation is $C_p - C_v = \frac{R}{M}$ where $M$ is the molar mass of the gas in kg/mol.

4. For nitrogen gas $N_2$, $M = 28\,\text{g/mol} = 28 \times 10^{-3}\,\text{kg/mol}$

5. Therefore, $C_p - C_v = \frac{R}{28 \times 10^{-3}}$ If one uses gram-based mass units as implied by the options, this is written as $C_p - C_v = \frac{R}{28}$

6. Hence the correct option is $\boxed{\text{B}}$

Option check

• A: $28R$ — incorrect
• B: $R/28$ — correct
• C: $R/14$ — incorrect
• D: $R$ — incorrect