Consider the experiment of Gay-Lussac: A cylinder is split into two compartments $A$ and $B$ by a barrier. Compartment $A$ initially contains some gas and compartment $B$ is initially empty. The walls of the cylinder as well as the barrier are assumed to be adiabatic.
Experiment shows that if a small opening is made in the barrier, allowing the gas to pass between the two compartments, then after some time the gas will fill the whole volume of the cylinder. Indeed it's a well-known property of gases that they fill the entirety of the volume of the container in which they are confined.
During this transformation, no heat is added to the gas, and no work is done on it either. Also the net external force on the gas is zero. Initially, the center of mass of the gas is at rest, located at some point in the interior of compartment $A$. But since the gas fills the whole volume of the cylinder at equilibrium, the center of mass must move.
But if the net external force on the gas is zero, the center of mass should always remain in the same place, no?
Best Answer
Gas molecules have temperature, which means speed. There are trillions of them, shooting around, bouncing off each other and the walls. If you remove the barrier, the molecules that had been bouncing off it keep going into the empty part. And the ones that would have bounced off those also keep going. Basically, the randomness means that the probability of not filling the empty space, while not zero, is maybe 10^-kajillion.
And yes, the center of mass will remain in the same place, meaning that the entire container will move a certain distance.
How? you might ask. Because in the interval of time before the empty part filled up, the pressure inside was unbalanced, making it move. And when the gas sloshed up against the opposing wall, the motion stopped.
That's how rockets work. There is no opposing wall.
There are (yes there are) people who think rockets could not work in vacuum because there's no air to push against. They would just "fizzle" :)