For the same raise in temperature of two moles of gas at constant pressure, the heat required for triatomic gas is K times the heat required for  monoatomic gas. The value of K is

molar specific heat of gas at constant pressure for tri atomic gas (6° of freedom)

${\text{C}}_{\text{p}}\text{=4R}$

$$\begin{gathered} molar specific heat of gas at cons\tan t pressure is {\text{C}}_{\text{p}} \\ {\text{C}}_{\text{p}}\text{=}\frac{5}{2}\text{R for monoatomic gas} \end{gathered}$$

$heat required for raise in temperature of gas at cons\tan t pressure is Q=n{\text{C}}_{\text{p}}\text{∆T}$

$Q_{triatomic}=k{Q}_{monotomic} substitute the values$

$n\left(4R\right)\text{∆T=kn(}\frac{5R}{2}\text{)}∆T$

$\therefore \text{K=}\frac{\text{4R}}{\frac{\text{5}}{\text{2}}\text{R}}\text{=}\frac{8}{5}$

Heat required is $\frac{8}{5}$  times.