Scuba Tanks and Air Pressure Equalization Temperature

I have been studying thermodynamics and couldn't find the answer in the ideal piston compressing/expansion gas law. The piston compressing the gas and heating up under Cv is ok, but if we use a receiver at ambient temp and x pressure and open a connecting valve to another receiver at lower pressure; there will be an expansion in the lower pressure receiver as air is rushed in and at the same time a compression raising the receiver pressure ... I think, and at the beginning of expansion the delta p is big but as pressure equalize the expansion is less but compression is greater thus generating more heat ... I think

make sense ?

Dan

<...if we use a receiver at ambient temp and x pressure and open a connecting valve to another receiver at lower pressure; there will be an expansion in the lower pressure receiver as air is rushed in and at the same time a compression raising the receiver pressure ...>

This is incorrect. There is actually an expansion in the higher pressure vessel and a compression in the lower pressure one.

Your right, the high pressure receiver will decrease in pressure and cool down.

When you open a valve from a receiver to Atm; the air comes out cooler to the point of freezing the valve, because there is a difference of pressure between the receiver and the Atm pressure.

Take the assumption that the same process happens when you fill up a reservoir with another one; at the beginning the lower pressure reservoir is at Atm pressure, the difference of press. is high so the air expand in the lower reservoir but as the pressure build up the difference is less, assuming the filling is long enough that pressure doesn't build up faster than the exchange of temperature.

what do you think?

The answer is the "Joule Thompson Effect" as per another thread answer:

The observed cooling occurs as a result of adiabatic expansion of the compressed air. The air, as it escapes from the valve, does work on the atmosphere by pushing it away against atmospheric pressure to make room for the expanded air. The amount of work done, delta W, equals P(atm) * delta V (the extra volume that the expanded air takes). We assume delta Q = 0 (adiabatic process), and so this work is done at the expense of internal energy of the expanding air which is why it cools down, expansion occurs because the 'empty space' on the boundary is more likely to get occupied by one of the more densely occuring from the high pressure reservoir molecules first.

<...expansion occurs because the 'empty space' on the boundary is more likely to get occupied by one of the more densely occuring from the high pressure reservoir molecules first...>

This statement makes no sense.

In the case of two vessels connected via a valve, expansion in the higher pressure vessel occurs because the gas is leaving it via the valve.