A turbine discharges $200k\frac{g}{h}$ of saturated steam at $10$ bar absolute$.$ It is desired to generate steam at $250C$ and $10$ bar by mixing the turbine discharge with a second stream of superheated steam of $300C$ and $10$ bar.

a$.$ If $300k\frac{g}{h}$ of the product steam is to be generated, how much heat must be added to the mixer?

b$.$ If instead the mixing is carried out adiabatically, at what rate is the product steam generated?