Cryogenic distillation is a process where oxygen is separated from the air in a separation column at low temperatures for medicinal use. In stationary state they are fed to column $100$mol$/$s air at room temperature and pressure, and partially condensed to reach $90$K and $5$ atm conditions. The output liquid current contains $95\%$ oxygen, and the vapour current contains $10\%$ oxygen. Determine:

a$)$ Molar flow of the vapour stream from the condenser: mol$/$s

b$)$ Molar flow of the liquid current from the condenser: mol$/$s

c$)$ Heat transferred in the cryogenic distillation column: kW

Data for liquid oxygen, density$=1143$kg$/$m$3,$ Cp $=2\mathrm{.}4$ kJ$/$KgK

Data for liquid nitrogen, density $=745\mathrm{.}5$kg$/$m$3,$ Cp $=2\mathrm{.}2$ kJ$/$KgK