$1.$ A gas stream containing $40$ mol $\%$ H$2,40$ mol $\%$ CO$2$ and the balance water vapor at $500\backslash$deg C fed to a condenser at a rate of $2\mathrm{.}5$ SCMH$.$ The gas and liquid streams leaving the condenser are in equilibrium at $15$oC and $1$ atm. Assume that all of the water vapor is condensed to liquid water $($not a good assumption$)$ and that there is no dissolved gases in the condensed water.

a$)$ Draw and label the above process flow diagram completely.

b$)$ Calculate the rate $($kw$)$ at which heat must be transferred from the condenser.

c$)$ Show that the assumption of total condensation of the water vapor is invalid