Question $3$

A compression is carried out in $3$ different ways which brings an air$-$fuel mixture from state $1$ to state $2$ with:

State $1$: $P_1=2$ bar $V_1=4$ liters

State $2$ : $P_2=4$ bars $V_2=2$ liters

The first evolution is isochoric then isobaric, the second isobaric then isochoric, the third is such that P$.$V $=$ Cte. $($isothermal$)$

Represent the $3$ transformations in Clapeyron coordinates.

Calculate the work in the $3$ cases.

Which transformation will we choose if we want to spend the least motor $($driving$)$ energy?