re: That maybe true, but
Why does it sound unreasonable to you?
Some information from:
http://resources.schoolscience.co.uk/BAMA/16plus/aerosch2pg5.html
Free expansion The same reasoning will work for a gas that is expanding freely. Rather than bouncing off a container, the particles bounce off each other. But they are all moving outwards. So any collisions at the edges of the gas will have the effect of taking some of the speed off the expanding molecules. You can also think of it that some of the kinetic energy of the particles is being taken away to push the gas into a bigger volume. I.e. the gas particles have to do work to expand. This reduces the average KE and therefore the gas cools.