For hydrogen gas ${\text{C}}_{\text{p}}{\text{–C}}_{\text{v}}\text{=a}$ and for oxygen gas ${\text{C}}_{\text{p}}{\text{–C}}_{\text{v}}\text{=b}$ so the relation between a and b is given by(where C_p and C_v are gram specific heats).

Relation between specific heat per unit mass $C_p-C_v=\frac{R}{M}$

For Hydrogen $a=\frac{R}{M\left(H\right)}=\frac{R}{2}\mathrm{........}\left(1\right)$

For Oxygen $b=\frac{a}{M\left(O\right)}=\frac{R}{32}\mathrm{........}\left(2\right)$

$\frac{a}{b}=\frac{\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$32$}\right.}=\frac{32}{2}=16\Rightarrow a=16b$