Answer
a) 1/3
b) 2/3
Work Step by Step
(a) We know that
$Work\space done=Q_h-Q_c$
$\implies Work\space done=Q_h-\frac{2Q_h}{3}=\frac{Q_h}{3}$
Now $\eta=\frac{Work\space done}{Heat\space input}$
$\eta=\frac{\frac{Q_h}{3}}{Q_h}=\frac{1}{3}$
(b) As $\eta=1-\frac{T_c}{T_h}$
$\frac{1}{3}=1-\frac{T_c}{T_h}$
$\implies \frac{T_c}{T_h}=\frac{2}{3}$
