In article , Richard J Kinch
says...

Compressed air exiting an orifice gets colder (temperature decreases) from
expansion, while gaining some new heat from the friction and turbulence of
passing through the orifice.

In that case, it's a simple accounting job to see that
the warming from friction is much smaller than the
cooling from expansion. The gas is not 'cooling as
it gains heat.' The NET change in internal heat is
negative.

It's simply cooling. The resulting container of colder
gas contains less internal heat after the expansion.

The internal energy of a gas is a simply proportional
to 3/2 kT. Hotter gas has always has more internal
heat energy.

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