Problem $7(25$ points$)$

Steam steadily enters a turbine at a rate of $90,000k\frac{g}{h}r$ through an inlet flow area of $109c{m}^2$ at $600C$ and $6000$ kPa $.$ The steam leaves the turbine through an outlet flow area of $985c{m}^2$ as saturated vapor at $200$ kPa $.$ Heat is lost from the turbine to the surroundings at a rate of $600k\frac{J}{s}.$ Determine:

a$)$ the average velocity of the steam at the inlet $(\frac{m}{s})$;

b$)$ the average velocity of the steam at the outlet $(\frac{m}{s})$;

c$)$ the temperature of the steam at the outlet $(C)$; and

d$)$ the rate of work output of the turbine $($ kW $).$