For carbon dioxide, number of moles $\left({\mathrm{n}}_1\right)=\frac{22}{44}=\frac{1}{2}$

Molar specific heat of $\mathrm{C}{\mathrm{O}}_2$ at constant volume ${{\mathrm{C}}_{\mathrm{V}}}_1=\frac{5\mathrm{R}}{2}$

For oxygen, number of moles $\left({\mathrm{n}}_2\right)=\frac{16}{32}=\frac{1}{2}$

Molar specific heat of ${\mathrm{O}}_2$ at constant volume ${{\mathrm{C}}_{\mathrm{V}}}_2=\frac{5\mathrm{R}}{2}$

Let $\mathrm{T} \mathrm{K}$ be the temperature of mixture.

Heat lost by ${\mathrm{O}}_2$ = Heat gained by $\mathrm{C}{\mathrm{O}}_2$

${\mathrm{n}}_2{{\mathrm{C}}_{\mathrm{V}}}_2∆{\mathrm{T}}_2={\mathrm{n}}_1{{\mathrm{C}}_{\mathrm{V}}}_1∆{\mathrm{T}}_1$

$\frac{1}{2}\mathrm{ }\left(\frac{5}{2}\mathrm{ }\mathrm{R}\right)\left(310-\mathrm{T}\right)=\frac{1}{2}\times \left(\frac{5\mathrm{R}}{2}\right)\left(\mathrm{T}-300\right)$

$2\mathrm{T}=610$

$\mathrm{T}=\frac{610}{2}=305 \mathrm{K} = 32 °\mathrm{C}$