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12 . kinetic theory of gases — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics12 . kinetic theory of gases1 Mark
MCQ
The molecules of a given mass of a gas have a $r.m.s.$ velocity of $200\, m/sec$ at $27°C$ and $1.0 \times {10^5}\,N/{m^2}$ pressure. When the temperature is $127°C$ and pressure is $0.5 \times {10^5}\,N/{m^2}$, the $r.m.s.$ velocity in $m/sec$ will be
  • A
    $\frac{{100\sqrt 2 }}{3}$
  • B
    $100\sqrt 2 $
  • ✓
    $\frac{{400}}{{\sqrt 3 }}$
  • D
    None of the above
✓

Answer

Correct option: C.
$\frac{{400}}{{\sqrt 3 }}$
c
We know that: $v \propto \sqrt{ T }$

$\Rightarrow \frac{ v }{200}=\sqrt{\frac{400}{300}}$

$\Rightarrow v =\frac{200 \times 2}{\sqrt{3}}=\frac{400}{\sqrt{3}} \; m / s$

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