Answer
(a) $Q = 450 J $
(b) $W = -450J$
(c) $\Delta U = 675 J$
Work Step by Step
(a) If the gas is isothermal, $\Delta T = 0$ so
$\Delta U = nC_VΔT = 450 J $ Hence
$Q = ΔU +W $
$Q = 0 + 450 J $
$Q = 450 J $
(b) For adiabatic,
$Q = 0$
$0 = +450J +W $
$W = -450J$
Hence, $\Delta U = W = -450J$
(c) For isobaric, the pressure is constant, $\Delta V = 0$
We take $W = p\Delta V = nR \Delta T $
So $\Delta T = \frac{p \Delta V}{nR} = \frac{W}{nR}$
Now $Q = n\frac{5}{2}R \Delta T$
$Q = n\frac{5}{2}R(\frac{W}{nR})$
$Q = \frac{5}{2} W$
$Q = \frac{5}{2} (450 J)$
$Q = 1125 J $
Thus, $\Delta U = Q - W $
$\Delta U = 1125 J - 450 J $
$\Delta U = 675 J$
