A$.$ You are a chemical engineer in charge of a process using an open feedwater heater. You flow superheated steam into your process along with two liquid water streams, with the goal of creating a saturated vapor. The following parameters hold for your system:

P $($supper heated steam$)-300$ bar.

T $($supper heated steam$)-600$ degree C

Flow rate $($supper heated steam$)30$ kg$/$s

P $($liquid water $1)-150$ bar

T $($Liquid water $1)-20$ degree C

Flow rate $($Liquid $1)-4$ kg$/$s$.$

P $($liquid water $2)-50$ bar

T $($Liquid water $2)-0$ degree C

Flow rate $($Liquid $2)-2$ kg$/$s$.$

The temperature surrounding the system is a comfortable $28\backslash$deg C$.$ The system may be assumed to be at steady state. The saturated steam leaves at $80$ bar.

$1)$ Determine the final temperature of the saturated steam $($in Celsius$).$

$2)$ Perform an energy balance and calculate the amount of heat removal Q needed to achieve our saturated steam conditions.

$3)$ Calculate the rate of entropy generation resulting from this system.

B$.$ Now your output steam from part $($a$)$ is to be put through a nozzle with a steam velocity of $40$ m$/$s$.$ The pressure at the end of the nozzle is $40$ bar. Furthermore, the system is not adiabatic, with $10,000$ kJ$/$s of heat constantly added to the steam. The surrounding temperature is still $28\backslash$deg C$.$ Assume the process is reversible.

$1)$ Calculate the specific entropy of the exiting steam.

$2)$ Determine the final temperature of the exiting steam.

$3)$ Determine the velocity of steam leaving the nozzle