$3)$ A piston$-$cylinder containing Refrigerant $22$ executes a Carnot refrigeration cycle between:

Process $1=>2$: Isothermal expansion

Process $2=>3$: Adiabatic compression

Process $3=>4$: Isothermal compression

Process $4=>1$: Adiabatic expansion

The refrigerant is adiabatically compressed from $1\mathrm{.}5$ bar and $\backslash (-20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ then isothermally compressed to a saturated vapor at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Fix the states and draw the corresponding p$-$v diagram for this process. Use the $\backslash (1^\{\backslash$text $\{$st $\}\}\backslash )$ and $\backslash (2^\{\backslash$text $\{$nd $\}\}\backslash )$ laws to calculate the work and heat transfer per unit mass for each process. $(16$ pts$)$