Temperature is base on the average kinetic motion of all atoms

[ntc2019]

Sorry for this silly question , I am still high school student . I know that temperature is base on the average kinetic motion of all atoms. But kinetic motion is not absolute so in what case should we use this formula: v= $$\sqrt{\frac{3RT}{\mu}}$$ . Should it be the velocity in respect to the center of mass? In that case , two objects have the same average velocity may have different temperature like that when we open a box fill with vacuum and close it fast enough when the temperature inside that box is different from outside because the air only go in the box in one way . Thank you for reading my question .

 

[Aaron Barnard]

The formula you have given is for the root mean square (RMS) velocity of a gas particle in an ideal gas. It does not apply to the situation you describe with a box filled with air and then closed quickly. The temperature inside the box would be different from the outside because the air molecules inside the box are colliding with each other, transferring energy from one to another, which increases the temperature. This process is known as the equipartition of energy.