$$ A hot$-$water stream at $80\backslash$deg C enters a mixing chamber with a mass flow rate of $0\mathrm{.}5$ kg$/$s where it is mixed with a stream of cold water at $20\backslash$deg C$.$ If it is desired that the mixture leave the chamber at $42\backslash$deg C$,$ determine the mass flow rate of the cold water stream. Assume all the streams are at a pressure of $250$ kPa.

$$ Calculate using specific heat.

$$ Calculate using Steam tables

$$ Compare results: Pros and cons of each method.