question_answer 21)

                  A vessel of volume V contains a mixture 1 mole of Hydrogen and 1 mole of Oxygen (both considered as ideal). Let \[{{f}_{1}}(\upsilon )d\upsilon ,\] denote die fraction of molecules with speed between \[\upsilon \] and \[(\upsilon +d\upsilon )\] with \[{{f}_{2}}(\upsilon )d\upsilon ,\] similarly for oxygen. Then                 (a) \[{{f}_{1}}(\upsilon )+{{f}_{2}}(\upsilon )\] obeys the Maxwell?s distribution law.                 (b) \[{{f}_{1}}(\upsilon ),\,\,{{f}_{2}}(\upsilon )\] will obey the Maxwell?s distribution law separately.                 (c) Neither \[{{f}_{1}}(\upsilon ),\] nor \[{{f}_{2}}(\upsilon )\] will obey the Maxwell's distribution law.                 (d) \[{{f}_{2}}(\upsilon )\] and \[{{f}_{1}}(\upsilon )\] will be the same.

Answer:

                  (b) \[f(\upsilon )=\,\,4\pi \,{{\left( \frac{M}{2\pi RT} \right)}^{3/2}}\,{{\upsilon }^{2}}\,{{e}^{-m{{\upsilon }^{2}}/2RT}}\]