a
(a)
Heat at constant pressure
$\Delta Q=n C_p \Delta T$
Heat for doing work
$\Delta W=n R \Delta T$
Then $\frac{\Delta W}{\Delta Q}=\frac{n R \Delta T}{n C_P \Delta T}$
$\frac{\Delta W}{800}=\left(\frac{\gamma-1}{\gamma}\right)$
$\frac{\Delta W}{800}=1-\frac{1}{\gamma}$
$\frac{\Delta W}{800}=1-\frac{3}{4}$
$\Delta W=200 \,cal$