Why does an LPG tank get cold as gas is used?

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Hi all, I am having trouble grasping the phenomenon on why the LPG tank freezes as you use up more and more of the gas inside.

My understanding is this. Initially, the tank is full of liquefied gas, and as you use up the gas, the pressure inside the tank drops, and since the temperature inside the tank did not change, the liquid should flashes into gas. But I don't understand how this can make the tank itself become cold? Is it maybe because the liquid inside the tank used the surrounding energy to change into gas?

Thanks.
 
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the liquid inside the tank used the surrounding energy to change into gas

Well done.
The energy to change state has to come from somewhere and the tank is not a closed system.

BTW: strictly speaking the LPG tank does not freeze - what happens is that ice forms on the outside of the tank.
 
This also happens with a compressed air tank where there is no phase change. It turns out that the cooling happens because the gas "does work" on the surrounding atmosphere as it expands - it is not exactly like pushing on a solid boundary but somewhere in between that and free expansion.