Throughout my physics education this far, I have always understood that adiabatic expansions and compressions involving ideal gases are reversible and follow $pV^\gamma = $ constant, provided the process is quick enough.
However, this year my thermodynamics notes contain the following:
"In rapid adiabatic expansion, the gas ends up moving fast as a fluid – i.e. some U is converted not to work on the piston, but KE of the bulk fluid. When the expansion stops, unless you are very ingenious (e.g. in a gas turbine), this KE converts back to U as the fluid slops around in the container. If you then compress the gas slowly back to its original volume it will be warmer than it was at the start – ie the 1st expansion was irreversible"
Can anybody help me get my head around this? Isn't the internal energy of an ideal gas already defined to be the kinetic energy? If energy is conserved in the process, how can we end up with a hotter gas in the end?