$7$

$5.(15$ points$)$ Saturated steam enters the condenser of a steam power plant at $20$ kPa and a quality of $95\%$ with a mass flow rate of $20,000k\frac{g}{h}.$ It is to be cooled by water from a nearby river by circulating the water through tubes within the condenser. The river water enters at $5C$ and leaves at $15C.$ The entering steam leaves the condenser as a saturated liquid at $20$ kPa $.$

$($a$)$ Determine the required mass flow rate of the cooling water in units of $k\frac{g}{s}.$

$($b$)$ Calculate the rate of heat transfer from the steam to the cooling water in units of $k\frac{J}{s}.$