An Problem $6(25$ points$)$

An ideal gas $)=(28\mathrm{.}314\frac{J}{m}o\frac{l}{K}$ executed heat engine is running according to the circle of $12341$ shown in the PV diagram.

Steps $12$ and $34$ are constant volume and state $1$ and state $3$ have the same pressure, all four steps are reversible.

a$)$ Calculate the $Q_H,Q_C,$ and $W$ of this circle $($assume $1$mol of ideal gas$).$

b$)$ Calculate the efficiency of the circles.

c$)$ If steps $12$ and $34$ are changed to reversible adiabatic compression and expansion, respectively. What is the efficiency of the circle?

Hint: First use the equation of state to identify the relationships among PVT at each state example: from step $12($constant volume process$)$ we will find $P_2=2P_1.$