(D) The formula for $rms$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Given that the $rms$ speed of $H_2$ at temperature $T$ is equal to the $rms$ speed

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(D) The formula for $rms$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Given that the $rms$ speed of $H_2$ at temperature $T$ is equal to the $rms$ speed of $N_2$ at $T_2 = 27^{\circ}C = 300 \ K$.So,$\sqrt{\frac{3RT}{M_{H_2}}} = \sqrt{\frac{3RT_2}{M_{N_2}}}$.Squaring both sides: $\frac{T}{M_{H_2}} = \frac{T_2}{M_{N_2}}$.Given $M_{N_2} = 14 \times M_{H_2}$.Substituting the values: $\frac{T}{M_{H_2}} = \frac{300}{14 \times M_{H_2}}$.$T = \frac{300}{14} \approx 21.4 \ K$.

Class 11 Physics Kinetic Theory of Gases Speed (velocity) of Gas (rms, mean and Most probable speed)

Easy

The $N_2$ molecule is $14$ times heavier than the $H_2$ molecule. At what temperature will the $rms$ speed of $H_2$ molecules be equal to the $rms$ speed of $N_2$ molecules at $27^{\circ}C$?

A
$50^{\circ}C$
B
$40^{\circ}C$
C
$87^{\circ}C$
D
$21.4 \ K$

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Kinetic Theory of Gases

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Speed (velocity) of Gas (rms, mean and Most probable speed)

If a gas is compressed isothermally,then the r.m.s. velocity of its molecules

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The $N_2$ molecule is $14$ times heavier than the $H_2$ molecule. At what temperature will the $rms$ speed of $H_2$ molecules be equal to the $rms$ speed of $N_2$ molecules at $27^{\circ}C$?

Similar Questions

If a gas is compressed isothermally,then the r.m.s. velocity of its molecules

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The temperature at which oxygen molecules will have the same r.m.s. speed as helium molecules at $57^{\circ} C$ is (molecular masses of oxygen and helium are $32$ and $4$ respectively.) (in $K$)

At what temperature $(K)$ will the $r.m.s.$ velocity of hydrogen gas be equal to the escape velocity from the Earth?

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