Suppose a box of idel mono-atomic gas has reference frame velocities V xav , V yav and V zav , then at equilibrium the atoms of the ideal gas have three average velocities. Now define the rms velocities as
V x rms = sqrt [ sum over all atoms(Vx - V xav)^2 ]/N and the following for y and z, where the sums are over N which is equal to billlions and billions of atoms. The thermal temperature of the gas is given by V x rms (for y,z too) and not V x av(for y,z also) and therefore has no direct connection to the reference frame velocity.
Suppose a box of idel mono-atomic gas has reference frame velocities V xav , V yav and V zav , then at equilibrium the atoms of the ideal gas have three average velocities. Now define the rms velocities as
V x rms = sqrt [ sum over all atoms(Vx - V xav)^2 ]/N and the following for y and z, where the sums are over N which is equal to billlions and billions of atoms. The thermal temperature of the gas is given by V x rms (for y,z too) and not V x av(for y,z also) and therefore has no direct connection to the reference frame velocity.