I am currently studying Thermodynamics from Khan Academy.
In one of their videos, Sal explains how the free expansion of a gas doesn't change the temperature of the system because the average kinetic energy of the molecules of the gas doesn't change during the expansion. I've a question regarding this.
Consider a fixed amount of gas inside a box. Say this box is inside a box that is 10000 times in volume than our original box. I then disappear the walls of our original box and the gas starts to expand throughout the large box. In this case also, the average kinetic energy of the molecules stay the same.
Does this mean that the temperature wouldn't be reduced?
It clearly doesn't seem so.
Say I use a thermometer having an initial reading of $T_0$ such that $T_0<T$ to test the temperature before and after expansion. The thermometer registers temperature $T$ before expansion because the gas molecules are able to increase the kinetic energy of the particles in the thermometer to report $T$. If I test temperature using the thermometer after expansion from an arbitrary point in the box, there wouldn't be as much molecules hitting the thermometer to raise its temperature to report $T$.
Would the thermometer still report $T$ after a considerable amount of time, knowing that the gas has expanded very much?
Would the temperature of the system still be $T$ after the expansion?