Answer
a) $\Delta U_{ac}=-84J$
b) $W_{dc}=28J$
c) $Q_{cda}=-112J$
d) $U_{ac}=-140J$
e) $Q_{da}=-156J$
Work Step by Step
a) $\Delta U_{ac}=Q_{ac}-W_{ac}=-175J-(-35J)=-140J$
$Q_{abc}=\Delta U_{abc}+W_{abc}=-140J+56J=-84J$
b) $W_{bc}=0$
$W_{cda}=W_{cd}=P_c\Delta V_{cd}=P_c(V_c-V_d)$
$P_c(V_d-V_c)=-\frac{1}{2}P_b(V_a-V_b)=-\frac{1}{2}W_{abc}=-\frac{1}{2}(-56)=28J$
c) $Q_{cda}=\Delta U_{cda}+W_{cda}=-140J+28J=-112J$
d) $U_a-U_c=U_{ac}=-140J$
e) $U_d=U_c+12J$
$U_{da}=U_a-U_c-12J=\Delta U_{ac}-12J=-156J$
$Q_{da}=U_{da}+W_{da}=-156J$