$(65)2.$ A heat exchanger uses $25k\frac{g}{h}$ of high pressure steam at $\frac{40}{b}ar$ and $350C$ to heat and vaporize a liquid aniline stream as shown in the figure below. The steam condenses completely in the heat exchanger and exits as saturated condensate at $39$ bar. The heat capacity of liquid aniline is approximated by the following equation: $C_p=178+0\mathrm{.}394T,$ where $T$ is in $C$ and $C_p$ is in $\frac{J}{m}ol-C.$

a$)$ What is the heat duty of the exchanger in $kW($i$.$e$.,$ how much energy is provided by the steam$)?(25$ pts$)$

b$)$ What is the flowrate of aniline in $k\frac{g}{h}?(40pts$