Opening Tank Valve

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Slam open the valve however and the compression happens quickly, and there is simply not enough time for the heat energy to escape from the gas, so the gas itself gets to a higher temperature.
Higher than what? Seems like it expands as it enters the hose, becoming colder. Pressure drops from the IP to <something>. As you say, it then compresses, but only back up to the IP, right? How does it get hotter than it was originally?
 
Sorry, i should have been clearer in my explanation!

The gas that enters and pressurises the 1st stage indeed intially cools down as it enters, but then as it gets pushed back up to pressure by the gas continuing to flow in, it warms back up again. Yes, heat is lost and it's final temperature is slightly less than it was in the tank (which reflects the word done on that gas)

The gas that "matters" is the gas that is already at ambient temperature and pressure sitting in the 1st stage, that gets shunted along and pressurised by the gas entering that stage from the cylinder. This gas starts at ambient temp, so as it gets compressed it heats up signficantly if it doesn't have enough time to reject that heat to the walls of the 1st stage containing it!
 
Thanks for the elaboration!
 
They do however not have momentum as their relative speed/angular speed is zero.
The needles /pointers and mechanisms in gauges do have momentum, once they are moving which is what the do as you open the valve. This momentum can cause them to overtravel when the pressure stops rising meaning the pointer no longer indicated the correct pressure
 
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