Q21 of 31 Page 94

A gas mixture consists of molecules of types A, B and C with masses mA > mB > mC . Rank the three types of molecules in decreasing order of (a) average K.E., (b) rms speeds.

Given:



(a) average kinetic energy of translation of molecule is given by



Where


T=temperature of molecule


k=Boltzmann constant


Thus, the average kinetic energy of translation depends only upon the temperature and is independent of mass of molecule.


Therefore, kinetic energy of all molecules are same


(b) the root mean square speed of a molecule is given by



Where


k=Boltzmann constant


m=mass of molecule


from above eqn. we can see that



rms speed of molecule is inversely proportional to its mass


∴



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