Water at a flow rate of $2$kg$/$s enters a long section of pipe with a temperature of $25\backslash$deg C and a pressure of $100$ bars. The pipe wall is heated such that $105$ W are transferred to the water as it flows through the pipe.

$($a$)$ If the water leaves the pipe with a pressure of $2$ bars, what is its outlet temperature?

$($b$)$ What value of the outlet temperature would be obtained if Equation $8\mathrm{.}37$ were used for the calculation?