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12.Kinetic Theory of Gases
normal

$27°C$ તાપમાને અને $1 \,atm$ દબાણે હાઈડ્રોજન અને ઑક્સિજનના અણુઓ માટે ($\nu_{rms}$) / ($\nu_{rms}$) = .. .....

A

$1/4$

B

$16$

C

$1/16$

D

$4$

Solution

અહી $ {m_{{O_2}}} = 32\,g\,{(mol)^{ – 1}},\,\,\,{m_{{H_2}}}\, = \,2\,g\,{(mol)^{ – 1}},\,\,\,\,$

 ${\upsilon _{rms}}\, = \,\sqrt {\frac{{3\,\,{k_B}T}}{m}} $ પરથી ${({\upsilon _{rms}})_{{O_2}}} \propto \frac{1}{{\sqrt {{m_{{O_2}}}} }}\,\,\,…\,\,\,…\,\,\,…\,\,(1)\,\,\,\,\,$

${({\upsilon _{rms}})_{{H_2}}} \propto \frac{1}{{\sqrt {{m_{{H_2}}}} }}\,\,\,…\,\,\,…\,\,\,…\,\,(2)$

$\therefore \frac{{\,{{({\upsilon _{rms}})}_{{H_2}}}}}{{{{({\upsilon _{rms}})}_{{O_2}}}}}\,\, = \,\,\sqrt {\frac{{{m_{{O_2}}}}}{{{m_{{H_2}}}}}}  = \sqrt {\frac{{32}}{2}} \,\, = \,\,4\,\,\,\,\,\,\therefore \,\frac{{\,{{({\upsilon _{rms}})}_{{H_2}}}}}{{{{({\upsilon _{rms}})}_{{O_2}}}}}\,\, = 4$

Standard 11
Physics

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