1. Tardigrade
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  3. Physics
  4. The molecules of a given mass of a gas have r.m.s velocity of 200 ms-1 at 27° C and 1.0 × 105 Nm-2 pressure. When the temperature and pressure of the gas are respectively, 127° C and 0.05 × 105 Nm-2, the r.m.s. velocity of its molecules in ms-1 is

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Q. The molecules of a given mass of a gas have r.m.s velocity of $200 \, ms^{-1}$ at $27^{\circ} C$ and $1.0 \times 10^5 \, Nm^{-2}$ pressure. When the temperature and pressure of the gas are respectively, $127^{\circ} C$ and $0.05 \times 10^5 \, Nm^{-2}$, the r.m.s. velocity of its molecules in $ms^{-1}$ is

NEETNEET 2016Kinetic Theory

Solution:

$v \propto \sqrt{T} \Rightarrow \frac{v}{200} = \sqrt{\frac{400}{300}} \Rightarrow v = \frac{200 \times2}{\sqrt{3}} m/s $
$ \Rightarrow v = \frac{400}{\sqrt{3}} m/s$