Five grams of Helium having rms speed of molecules as 1000 m/s and 24 g of oxygen  having rms speed of 1000 m/s are introduced into a thermally isolated vessel. The  ratio of rms speeds of Helium and oxygen when thermal equilibrium is  attained is  N2 . Find N. Neglect the heat capacity of the vessel.

For Helium,  1000=3RT14×10−3⇒3RT1=4000For Oxygen,  1000=3RT232×10−3⇒3RT2=32000By internal energy conservation, U1+U2=U1'+U2' We know,  U=fnRT2So,  3254RT1+522432RT2=3254+522432RTThis gives  T=T1+T22After mixing, RMS speed of Helium is v1=3RTM1=3RT1+T22M1=4000+3200024×10−3=15002m/sFor Oxygen, v2=3RT1+T22MO=4000+32000232×10−3=7502m/s v1v2=150027502=2