(C) The root mean square speed $(v_{rms})$ of gas molecules is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas c

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Independent of its pressure but directly proportional to the square root of its Kelvin temperature

(C) The root mean square speed $(v_{rms})$ of gas molecules is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is the absolute temperature in Kelvin,and $M$ is the molar mass of the gas.From this expression,it is clear that $v_{rms}$ depends only on the temperature $(T)$ and the molar mass $(M)$ of the gas.It is independent of the pressure $(P)$ of the gas.Therefore,$v_{rms} \propto \sqrt{T}$.

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

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The root mean square speed of the molecules of a gas is

A
Independent of its pressure but directly proportional to its Kelvin temperature
B
Directly proportional to the square roots of both its pressure and its Kelvin temperature
C
Independent of its pressure but directly proportional to the square root of its Kelvin temperature
D
Directly proportional to both its pressure and its Kelvin temperature

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Kinetic Theory of Gases

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

At a temperature of $300 \ K$,the kinetic energy of $O_2$ is $6.21 \times 10^{-21} \ J$ and its $rms$ speed is $484 \ m/s$. What will be the kinetic energy and $rms$ speed at $600 \ K$?

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$A$ mixture of $2$ moles of helium gas (atomic mass $= 4 \ amu$) and $1$ mole of argon gas (atomic mass $= 40 \ amu$) is kept at $300 \ K$ in a container. The ratio of the rms speeds $\left(\frac{v_{\text{rms}} \text{ (helium)}}{v_{\text{rms}} \text{ (argon)}}\right)$ is:

IIT 2012

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At what temperature is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at $47^{\circ}C$ (in $; K$)?

MediumAIEEE 2002

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The molecules of a given mass of a gas have root mean square speeds of $100 \ m/s$ at $27^{\circ} \ C$ and $1.00 \ \text{atm}$ pressure. What will be the root mean square speeds of the molecules of the gas at $127^{\circ} \ C$ and $2.0 \ \text{atm}$ pressure?

Medium

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Find the $v_{rms}$ of nitrogen gas at $300 \ K$.

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The root mean square speed of the molecules of a gas is

Similar Questions

At a temperature of $300 \ K$,the kinetic energy of $O_2$ is $6.21 \times 10^{-21} \ J$ and its $rms$ speed is $484 \ m/s$. What will be the kinetic energy and $rms$ speed at $600 \ K$?

$A$ mixture of $2$ moles of helium gas (atomic mass $= 4 \ amu$) and $1$ mole of argon gas (atomic mass $= 40 \ amu$) is kept at $300 \ K$ in a container. The ratio of the rms speeds $\left(\frac{v_{\text{rms}} \text{ (helium)}}{v_{\text{rms}} \text{ (argon)}}\right)$ is:

At what temperature is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at $47^{\circ}C$ (in $; K$)?

The molecules of a given mass of a gas have root mean square speeds of $100 \ m/s$ at $27^{\circ} \ C$ and $1.00 \ \text{atm}$ pressure. What will be the root mean square speeds of the molecules of the gas at $127^{\circ} \ C$ and $2.0 \ \text{atm}$ pressure?

Find the $v_{rms}$ of nitrogen gas at $300 \ K$.

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