The verticla water tank, shown has uniform cross section, closed at the top and initial level of water in it is `4.5m` from bottom. The empty space of length `L` contains air at atmospheric pressure `(10^(5)Pa)`, that can be considered as an ideal gas. When the value at the bottom is opened, the level of water decreases by `0.5m` when the flow of water ceases though value remains opened. Neglecting any variation in temperature during the process find intial length of empty space `L` in cm. (`g=10m//s^(2)`, density of water = 1000 kg//m^(3)`)