Answer
$\frac{\Delta E_{int}}{nRT_1} = -0.89$
Work Step by Step
The change of internal energy is given by
$\Delta E_{int} = nC_V(T_3-T_2)$
Where $C_V = \frac{5}{2}R$,
and
$T_3-T_2 = \frac{T_1}{3.00^{0.4}} - T_1$
So,
$\Delta E_{int} =n\frac{3}{2}R (\frac{T_1}{3.00^{0.4}} - T_1)$
$\Delta E_{int} =n\frac{5}{2}R (0.644T_1 - T_1)$
$\Delta E_{int} =n\frac{5}{2}R (-0.356 T_1)$
$\Delta E_{int} =-0.89n R T_1$
$\frac{\Delta E_{int}}{nRT_1} = -0.89$ (Rounded off to two decimal places)
