Question

If for hydrogen $C_p-C_v=m$ and for nitrogen $C_p-C_v=n$, where $C_p$ and $C_v$ refer to specific heats per unit mass respectively at constant pressure and constant volume, the relation between $m$ and $n$ is (molecular weight of hydrogen$=2$ and molecular weight of nitrogen$=14$)

• A. $n=14m$
• B. $n=7m$
• C. $m=7n$
• D. $m=14n$

Answer 1

The correct option is C $m=7n$

For hydrogen, $C_P-C_V=\frac{1}{M_{H_2}}\frac{dQ}{dT}=m$

For nitrogen, $C_P-C_V=\frac{1}{M_{N_2}}\frac{dQ}{dT}=n$

$⟹\frac{m}{n}=\frac{M_{N_2}}{M_{H_2}}=\frac{14}{2}=7$