Answer
a) $W=13.7KJ$
b) $Q=0$
c) $\Delta U=-13.7JK$
Work Step by Step
(a) We know that
$\Delta U=n(\frac{3}{2}R)(T_f-T_i)$
We plug in the known values to obtain:
$\Delta U=(3.92mol)(\frac{3}{2})(8.31J/mol.K)(205^{\circ}C-485^{\circ}C)$
$\Delta U=-13.7KJ$
Now $\Delta U=Q-W$
$\implies \Delta U=0-W$
$\implies W=-\Delta U$
$W=-(-13.7KJ)$
$W=13.7KJ$
(b) We know that in an adiabatic process, the system is thermally insulated and no heat flows, so $Q=0$
(c) We know that
$\Delta U=Q-W$
$\Delta U=0-W$
$\implies \Delta U=-W$
$\Delta U=-13.7JK$
