A rigid, $12\mathrm{.}00-$L steam cooker is arranged with a pressure relief valve set to release vapor and maintain the pressure once the pressure inside the cooker reaches $150$ kPa $.$ Initially, this cooker is filled with water at $175$ kPa with a quality of $10$ percent. Heat is now added until the quality inside The cooker is $40$ percent. The water is stirred at the same time that it is being heated. Determine the minimum entropy change of the heat$-$supplying source if $100$ kJ of work is done on the water as it is being heated. Use steam tables. $($Round the final answer to four decimal places.$)$

The minimum entropy change of the heat$-$supplying source is

$q,k\frac{J}{K}.$