If it were possible for a gas in a container to reach the temperature 0 K, its pressure would be zero. Would the molecules not collide with the walls? Would they not transfer momentum to the walls?
No, the molecules of gas will neither collide nor transfer momentum.
First explanation
Kinetic energy of gas is given as
Where K. E=kinetic energy of gas
kB = Boltzmann constant
T = temperature of gas
So, if T=0K then kinetic energy will be zero. Which also means that molecules of gas will not move at all. Hence, they will neither collide or transfer momentum to walls of container.
Second explanation
One can also understand this from zero pressure point of view.
Pressure of an ideal gas given as
P= nmv2 ……... (i)
Where n=number of molecules of gas per unit volume
m=mass of molecule of gas
v= velocity of gas molecule
And momentum is given as
Momentum= mass
velocity …...(ii)
From equation (i) and (ii), we can conclude that if pressure is zero,
velocity of molecules will be zero and hence momentum will be zero.