At STP, $22.4 \mathrm{L}$ of any gas is equal to $1 \mathrm{mol}$

$\therefore 5.6 \mathrm{L}=\frac{5.6}{22.4}=\frac{1}{4} \mathrm{mol}=n$.

In adiabatic process, $T{V}^{\gamma -1}=$ constant

$\therefore T_2{V}_2^{\gamma -1}=T_1{V}_1^{\gamma -1}$or $T_2=T_1{\left(\frac{V_1}{V_2}\right)}^{\gamma -1}$

For monoatomic (Helium) gas, $\gamma =\frac{C_p}{C_V}=\frac{5}{3}$

$\therefore T_2=T_1{\left(\frac{5.6}{0.7}\right)}^{\frac{5}{3}-1}=4T_1$

Further, in adiabatic process,

$Q=0\Rightarrow W+\Delta U=0$

or $W=-\Delta U=-n{C}_V\Delta T$

$=-n\left(\frac{R}{\gamma -1}\right)\left(T_2-T_1\right)$

$=-\frac{1}{4}\left(\frac{R}{\left(\frac{5}{3}\right)-1}\right)\left(4T_1-T_1\right)=-\frac{9}{8}R{T}_1$