Question:

A gas molecule of mass m at the surface of the Earth has kinetic energy equivalent to 0°C. If it were to go up straight without colliding with any other molecules, how high would it rise?

273kB2Mg

546kB3Mg

819kB2Mg

Answer is D
Average translational kinetic energy of molecules = KE = 3/2kBT = 819/2kB as T = 273K
Now, KE = PE
Or, 819/2kB = mgh
h = 819kB/2Mg