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CyanPhysics

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I have a problem that i cannot solve despite my best efforts. I do realize not all information here is relevant, but i still included it so you could get the full picture.

Imagining we have a cylinder that is filled with dry air (normal air without water vapor) that has a fixed volume of 8,5 liters. The initial pressure is 300 bar (30000 kPa). After use the final pressure is 50 bar (5000 kPa), therefore the change in pressure is 250 bar (25000 kPa). This happens in a span between 20 to 30 minutes. The cylinder is depressurizing into a tube thru a valve that reduces the maximum pressure inside that valve to 50 bar (5000 kPa) and then another reduction valve, furthermore reducing to 5 bar (500 kPa) and then again to 1.25 bar (125 kPa) the final chamber is of a volume approximately 1 liter, the sizes of the chambers in between are unknown. The final chamber is a mask and the air flows out with every exhale. From observation we have seen that there is some cooling effect, that is not measured.

My question is what is the theoretically maximum possible change in temperature at the reduction valve 300 bar -> 50 bar, if we disregard other factors from the inside. I will conduct an experiment on this and record the results, but i am still interested in the theory behind it as it will help me in the future.

Gas is normal air without water vapor.

P

P

ΔP = 250 bar

V = 8.5 Liters

t ≈ 1500 second

ΔT = ? Kelvin

Imagining we have a cylinder that is filled with dry air (normal air without water vapor) that has a fixed volume of 8,5 liters. The initial pressure is 300 bar (30000 kPa). After use the final pressure is 50 bar (5000 kPa), therefore the change in pressure is 250 bar (25000 kPa). This happens in a span between 20 to 30 minutes. The cylinder is depressurizing into a tube thru a valve that reduces the maximum pressure inside that valve to 50 bar (5000 kPa) and then another reduction valve, furthermore reducing to 5 bar (500 kPa) and then again to 1.25 bar (125 kPa) the final chamber is of a volume approximately 1 liter, the sizes of the chambers in between are unknown. The final chamber is a mask and the air flows out with every exhale. From observation we have seen that there is some cooling effect, that is not measured.

My question is what is the theoretically maximum possible change in temperature at the reduction valve 300 bar -> 50 bar, if we disregard other factors from the inside. I will conduct an experiment on this and record the results, but i am still interested in the theory behind it as it will help me in the future.

Gas is normal air without water vapor.

P

_{1}= 500 barP

_{2}= 50 barΔP = 250 bar

V = 8.5 Liters

t ≈ 1500 second

^{____________________________________________}ΔT = ? Kelvin

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