$($c$)$ Steam at a pressure $2$ MPa and $400C$ expands in a turbine operating at steady state to $10$ kPa and a quality of $93\%.$ The heat transfer from the turbine to the environment is $85k\frac{J}{k}g.$ Neglecting the kinetic and potential energies at the inlet and exit of the turbine, determine:

$($i$)$ The actual and reversible work

$($ii$)$ The irreversibility of the process

$($iii$)$ The availability before and after expansion

$($iv$)$ The second law efficiency