Answer
a) $\Delta S_{total}=0.000273\ Btu/R$
$\Delta S_{total}\geq0\rightarrow\mbox{possible}$
b) $\Delta S_{total}=-0.000182\ Btu/R$
$\Delta S_{total}\lt0\rightarrow\mbox{impossible}$
Work Step by Step
Given: $Q_H=1\ Btu,\ T_H=1100\ R,\ T_L=550\ R$
For a 35% efficiency:
$Q_L=(1-\eta)Q_H$
$Q_L=0.65\ Btu$
$\Delta S_{total}=-\dfrac{Q_H}{T_H}+\dfrac{Q_L}{T_L}$
$\Delta S_{total}=0.000273\ Btu/R$
$\Delta S_{total}\geq0\rightarrow\mbox{possible}$
For a 60% efficiency:
$Q_L=(1-\eta)Q_H$
$Q_L=0.40\ Btu$
$\Delta S_{total}=-\dfrac{Q_H}{T_H}+\dfrac{Q_L}{T_L}$
$\Delta S_{total}=-0.000182\ Btu/R$
$\Delta S_{total}\lt0\rightarrow\mbox{impossible}$
