A mixture of $50$ mol$\%$ ethanol and methanol at $300\backslash$deg C and $101$ kPa is to be cooled to $160\backslash$deg C in a heat exchanger. To do this, it is brought into contact with a stream of saturated liquid at $100\backslash$deg C; the outlet water stream is found as saturated vapor at the same inlet pressure. Calculate the water flow required to cool $100$ kmol$/$h of mixture:

a$)$ If the exchanger is adiabatic.

b$)$ Assuming a heat loss of $5\%$ in the exchanger