You are correct in thinking that a change in pressure will change the temperature at which oxygen can be liquified. But no, increasing the pressure will raise the temperature at which oxygen becomes a liquid, not lower it. This is easiest to understand with a phase diagram, like this Oxygen phase diagram in the Engineering Toolbox.
The blue line marks where the transition between liquid oxygen and gaseous oxygen occurs, and you can see the standard boiling point of -183 C is at 1 atmosphere (1 bar). But if you follow the blue curve up to a higher temperature, like 10 bar, the temperature at which condensation from O₂(g) gas to O₂(l) occurs is 30 degrees higher, not lower: about -150 C.
So far as “does it evaporate when exposed to normal atm pressure”, if you had condensed the oxygen at the 10 bar higher pressure, and then suddenly released the pressure to atmospheric pressure, the temperature of liquid oxygen would be higher than the transition temperature at that pressure. Drop a line down from the blue curve at 10 bar, down to 1 bar, and you will see you are now on the gaseous side of the transition. So yes it would start evaporating. And yes, since the heat of vaporization of O₂(l) is positive, the evaporating oxygen would cool down the remaining liquid.
Comments
You are correct in thinking that a change in pressure will change the temperature at which oxygen can be liquified. But no, increasing the pressure will raise the temperature at which oxygen becomes a liquid, not lower it. This is easiest to understand with a phase diagram, like this Oxygen phase diagram in the Engineering Toolbox.
The blue line marks where the transition between liquid oxygen and gaseous oxygen occurs, and you can see the standard boiling point of -183 C is at 1 atmosphere (1 bar). But if you follow the blue curve up to a higher temperature, like 10 bar, the temperature at which condensation from O₂(g) gas to O₂(l) occurs is 30 degrees higher, not lower: about -150 C.
So far as “does it evaporate when exposed to normal atm pressure”, if you had condensed the oxygen at the 10 bar higher pressure, and then suddenly released the pressure to atmospheric pressure, the temperature of liquid oxygen would be higher than the transition temperature at that pressure. Drop a line down from the blue curve at 10 bar, down to 1 bar, and you will see you are now on the gaseous side of the transition. So yes it would start evaporating. And yes, since the heat of vaporization of O₂(l) is positive, the evaporating oxygen would cool down the remaining liquid.