${\mathrm{c}}_{\mathrm{p}}\mathrm{\&}{\mathrm{c}}_{\mathrm{v}}$ are specific heats at constant pressure and volume respectively. It is observed that ${\mathrm{c}}_{\mathrm{P}}-c_{\mathrm{V}}=\mathrm{a}$ for hydrogen gas ${\mathrm{c}}_{\mathrm{P}}-c_{\mathrm{V}}=b$ for nitrogen gas. The correct relation between a & b is

$\begin{array}{l}{\mathrm{C}}_{\mathrm{P}}-{\mathrm{C}}_{\mathrm{V}}=\mathrm{R},\text{ where }{\mathrm{C}}_{\mathrm{P}}\text{ and }{\mathrm{C}}_{\mathrm{V}}\text{ are molar specific heat capacities. }\\ given c_p,c_v are specific heats\\ c_p-c_v=\frac{R}{Molecular weight}\\ molecular weight of hydrogen =2 and nitrogen=28\\ \text{ As per the question, a }=\frac{\mathrm{R}}{2}; \mathrm{b}=\frac{\mathrm{R}}{28}\\ \Rightarrow 2a=28b\\ a=14b\end{array}$