Answer
$\Delta E_{total} = 0J $
Work Step by Step
For a full cycle, we find the internal energy in step $3 \rightarrow 1$
$\Delta E_{3\rightarrow 1} = nC_V (T_3 - T_1)$
$\Delta E_{3\rightarrow 1} = (2.00 mol)(\frac{3}{2} \times 8.314 J/k.mol) (300 K - 350K)$
$\Delta E_{3\rightarrow 1} = -1.25 kJ $
So total internal energy for full process is
$\Delta E_{total} =\Delta E_{1\rightarrow 2} + \Delta E_{2\rightarrow 3} + \Delta E_{3\rightarrow 2} $
$\Delta E_{total} = 0J + 1.25 kJ - 1.25 kJ$
$\Delta E_{total} = 0J $
