question_answer 35)

                  A gas mixture consists of molecules of types A, B and C with masses \[{{m}_{A}}>{{m}_{B}}>{{m}_{C}}\]. Rank the three types of molecules in decreasing order of (a) average K.E., (b) rms speeds.

Answer:

                  (a) Average K.E. of a molecule of a gas                 \[=\frac{3}{2}\,kT\]                 Thus, average K.E of a molecule is independent of its mass, therefore, molecules A, B and C will have the same average K. E       (a) \[{{\upsilon }_{rms}}\,\alpha \frac{1}{\sqrt{m}}\]                 Thus, \[{{({{\upsilon }_{rms}})}_{c}}\,>\,{{({{\upsilon }_{rms}})}_{B}}>\,{{({{\upsilon }_{rms}})}_{c}}\]