$($i$)$ A steady Carnot power cycle with water is executed under the saturation dome between the pressure limits of $20$ kPa and $2$ MPa $.$ Water changes from saturated liquid to saturated vapor during the heat addition. Calculate net cycle work output $($in $k\frac{J}{k}g).$

$($ii$)$ A refrigerator removes heat from a refrigerated space at $0C$ at a rate of $2\mathrm{.}2$ kW and rejects it to a warm environment at $20C.$ What is the minimum possible power input $($ kW $)$ based on the reversed Carnot cycle?