Problem $2(20\%)$

Steam enters a turbine with a pressure of $20$ bar. A temperature of $320C$ and a velocity of $150\frac{m}{s}.$ Saturated vapor at $85C$ exists with a velocity of $100\frac{m}{s}.$ At steady state, the turbine develops work equal to $400k\frac{J}{k}g$ of steam flowing through the turbine. Heat transfer between the turbine and its surroundings occurs at an average outer surface temperature of $300$ K $.$ Neglect the change in potential energy between inlet and exit.

$(8)$ Determine the Heat transfer between the turbine and its surrounding $(\frac{{}_a}{m},k\frac{J}{k}g)(5\%)$

Clearly show your steps to reach the final answer

$($b$)$ Determine the rate at which entropy is produced within the turbine per kg of steam flowing, in kJ$/$kg$$K $(10\%)$

Clearly show your steps to reach the final answer