Will there be a temp change in free expansion I did a little thought experiment, where I place an infinitely long beaker filled with some gas, which has a moveable piston at the open part. So if I place this beaker in vaccume, there will obviously be no work done on the system and hence no loss of energy due to the work done by the system (because the int pressure of the energy will obviously push the piston upwards).
So here's my main question:
If in the Beginning, let's say we have a certain amount of gas placed in the beaker such that the piston is just 1 cm above the base. But after infinite time the lid will probably be at infinity. So if a t=0, the gas occupies a limited space, won't the collisions be high and hence kinetic energy be high, which would mean the temperature of the system is high? But at t= infinity, the gas would occupy an infinite amount of volume which would mean that there are less collisions, so wouldn't this reduce the velocity of the molecules, hence reduce the kinetic energy, hence reduce the temperature?
I feel something is wrong over here because mathematically, I know there shouldn't be any change in int energy, therefore the temperature. So how do we justify this experiment?
In a real gas, the internal energy is the sum of the kinetic energy of the molecules and their potential energy of interaction. An ideal gas is the limit of real gas behavior in the limit of large molar volumes in which the potential energy of interaction of the molecules approaches zero. The kinetic energy of the molecules depends only on temperature, but the potential energy of interaction of the molecules depends on both temperature and specific volume. The temperature of an ideal gas does not change when subjected to free expansion, but it does change for a real gas.  So the deviation from ideal gas behavior caused by potential energy of interaction of the molecules is what causes the temperature of a real gas to change in free expansion.