P1 * V1 / T1 = P2 * V2 / T2 the Combined Gas Law

Why does ice form on outflow pipes of gas cylinders or storage tanks?

The reason you get ice on a propane tank when you are burning fuel or bleeding the gas is explained by the Combined Gas Law (CGL)

The law states that for any gas the Pressure times the Volume divided by the Temperature is a constant. Constant means it's always the same.

PV/T = k   

I think I can explain using a gas barbecue propane tank as an example.

First, you want lots of gas in the tank in order to cook for a while. To get the gas in you pressurize or squeeze it. (As you squeeze gas molecules closely together gas turns into a liquid, this is why you feel liquid sloshing around a propane tank after a re-fill)

A full gas cylinder starts at about 130 pounds per square inch (psi) of pressure at 72 degrees F. The pipes which the gas flows through run at a lower pressure. A regulator valve controls the flow between high pressure tank and lower pressure pipes. By limiting gas pressure in the pipe a regulator provides a controlled flow of gas over a long time.

With a regulator connected and burners open gas flows out through the burners because pressure in the pipe is higher than outside air pressure (about 14 psi), and as long as the pipes are at lower pressure than the tank gas continues to flow out.

With a full tank the pressure differential is large and gas flows out fast, we often hear it roaring out and see it burning bright blue. It takes us 7 to 8 days to burn a 5 gallon tank camping and by week's end the flow is very slow and quiet.

When gas flows out internal tank pressure drops slowly so the tank temperature will drop to preserve PV/T = k ratio. However the effect is not big and would not explain ice on the outflow pipes we see above.

Back to the barbecue, (assuming it's not windy) we see a fairly steady flame. This shows the volume of gas inside the hose is stable. Think about it this way, gas flows in and out of the hose at the same rate so the volume of gas does not change inside the hose, it changes in the tank.

The only way to preserve the "k" gas ratio in the outflow valve and pipe with a steep Pressure drop and no Volume change is for gas Temperature to drop. Remember PV/T = k, and k does not change.

So the gas flowing out needs to drop temperature quickly to obey the Law, which causes the outlet valve and pipes to become very cold. Water vapor in the air condenses on the ultra cold surfaces and freezes.

You see ice on those pipes when gas is flowing out because it's the Law!