Answer
$\Delta E_{int} = 1247.1 J = 1.25 kJ $
Work Step by Step
The change in internal energy for adiabatic process in step $2 \rightarrow 3 $ is in the following with $C_V = \frac{3}{2} $ and $n = 2.00 mol$
$\Delta E_{int} = nC_V (T_3 - T_2)$
$\Delta E_{int} = (2.00 mol)(\frac{3}{2} \times 8.314 J/k.mol) (350 K - 300K)$
$\Delta E_{int} = 1247.1 J = 1.25 kJ $