# Thermodynamics question: venting a tank of liquid oxygen

I am trying to figure out how you can subcool a dewar of liquid oxygen (vacuum insulated) just by releasing the pressure sitting on top of it. The liquid I am thinking of in this case is liquid oxygen, which boils at -297.33 F at 1 atm. Let's say I fill a dewar with LO2, then pressurize that dewar to 3 psig (using cold gaseous oxygen), and then let it reach thermal equilibrium. Now once I open to vent to let that gas on top of it vent to atmosphere, there should be adiabatic expansion of the liquid of the pressure decreases, which should then decrease the temperature. All I am trying to figure out is about how much of a temperature drop would be reasonable to expect by doing this.

Some conditions:
Total LO2 mass = 68,000 kg
P_initial = 3 psig = 17.7 psia
P_final = 0 psig - 14.7 psia
T_initial = let's say -297 F
T_final = ?

I assume I can use the pressure change to somehow figure out the density difference, but I haven't taken thermodynamics in a while, so I am stuck on which equations/assumptions to use.

Thanks for the help.