A homogeneous binary liquid mixture of A and B, which contains 60% component A by mole fraction and obeys Raoult's law, is subjected to a preheating before being sent to a flash distillation column at a pressure of 1000 Pa. It is known that 50% of the entering mixture is vaporized. Find the compositions of the vapor and liquid phases and the operating temperature of the column. The boiling temperatures of components A and B at 1000 Pa are 439 K and 459 K, respectively. The vapor pressures of the components are given by the following equations:

PA0=20.84T2210T21715400 lnPB0=19.94T1467T22072300