Question $2[5$ points$]$:

A hot$-$water stream at $80C$ enters a mixing chamber with a mass flow of $0\mathrm{.}5k\frac{g}{s}$ where it is mixed with a stream of cold water at $20C.$ If it is desired that the mixture leaves the chamber at $50C,$ determine $($a$)$ the mass flow rate of the cold$-$water stream and $($b$)$ the rate of entropy generation. Assume all the streams are at a pressure of $250$ kPa $.$