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