Coefficient of performance $=\frac{Q_{2}}{Q_{1}-Q_{2}}$
Substitute 800 for $Q_{1}$ and 500 for $Q_{2}$ in above expression.
Coefficient of performance $=\frac{500}{800-500}$
$=\frac{5}{3}$
$A \rightarrow B :$ Isothermal expansion at temperature $T$ so that the volume is doubled from $V _{1}$ to $V _{2}=2 V _{1}$ and pressure changes from $P _{1}$ to $P _{2}$
$B \rightarrow C :$ Isobaric compression at pressure $P _{2}$ to initial volume $V _{1}$
$C \rightarrow A$ : Isochoric change leading to change of pressure from $P _{2}$ to $P _{1}$
Total workdone in the complete cycle $ABCA$ is


Step $1$ It is first compressed adiabatically from volume $V_{1}$ to $1 \;m ^{3}$.
Step $2$ Then expanded isothermally to volume $10 \;m ^{3}$.
Step $3$ Then expanded adiabatically to volume $V _{3}$.
Step $4$ Then compressed isothermally to volume $V_{1}$. If the efficiency of the above cycle is $3 / 4$, then $V_{1}$ is ............ $m^3$
