An ideal gas, $C{P}_P=(\frac{7}{2})R$ and $C{V}_V=(\frac{5}{2})R,$ undergoes a cycle consisting of the following

mechanically reversible steps:

$($f$)$ An adiabatic compression from $P_1,V_1,T_1$ to $P_2,V_2,T_2$

$($g$)$ An isobaric expansion from $P_2,V_2,T_2$ to $P_3(=P_2),V_3,T_3$

$($h$)$ An adiabatic expansion from $P_3,V_3,T_3$ to $P_4,V_4,T_4$

$($i$)$ A constant volume process from $P_4,V_4,T_4$ to $P_1,V_1(=V_4),T_1$

Sketch this cycle on a PV diagram and determine its thermal efficiency if $T_1,T_2,T_3$ and $T_4$ are $500,$

$800,2000$ and $1000K,$ respectively. $($Hint: the thermal efficiency is defined as the ratio of net work

output to heat input$)$