A three$-$stage flash unit is being operated in a plant. The feed enters flash drum $2($FD$2).$ The vapour

from FD$2$ is cooled to a two$-$phase mixture and flashed in FD$1.$ The vapour from FD$1$ is taken out as a

product, while the liquid from FD$1$ is heated to the operating temperature of FD$2$ and returned to FD$2.$

The liquid from FD$2$ is heated to a two$-$phase mixture and introduced into FD$3.$ The liquid stream from

FD$3$ is taken out as a product, while the vapour from FD$3$ is cooled to the operating temperature of FD$2$

and returned to FD$2.$

The feed is $100k\frac{g}{h}$ liquid containing $40\%$ ethanol and the rest being water. This feed is heated to

$87C$ and enters FD$2.$ The flow rate and the composition of the vapour stream leaving stage $1$ is $50$

$k\frac{g}{h}$ and $0\mathrm{.}75,$ respectively. All the flash units are operating at $1k\frac{g}{c}{m}^2.$ Based on this information

calculate the following:

a$)$ Sketch the process. $[6$ points$]$

b$)$ What is the operating temperature of stages $1$ and $3?[15$ points$]$

c$)$ The flow rates and compositions of all streams leaving the three stages. $[15$ points$]2$