(A) The $r.m.s.$ velocity of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.This shows that $v_{rms} \propto \sqrt{T}$.The pre

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(A) The $r.m.s.$ velocity of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.This shows that $v_{rms} \propto \sqrt{T}$.The pressure does not affect the $r.m.s.$ velocity of an ideal gas.Given $T_1 = 27^o C = 300 \,K$ and $v_1 = 200 \,m s^{-1}$.Given $T_2 = 127^o C = 400 \,K$.Using the ratio: $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$.$\frac{v_2}{200} = \sqrt{\frac{400}{300}} = \sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}$.Therefore,$v_2 = 200 \times \frac{2}{\sqrt{3}} = \frac{400}{\sqrt{3}} \,m s^{-1}$.

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

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

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A
$\frac{400}{\sqrt{3}}$
B
$\frac{100\sqrt{2}}{3}$
C
$\frac{100}{3}$
D
$100\sqrt{2}$

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Class 11

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Kinetic Theory of Gases

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

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The $rms$ speed of gas molecules in a container is $400 \, ms^{-1}$. If half of the gas is removed at a constant temperature,the new $rms$ speed will be .... $ms^{-1}$.

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$A$ vessel is partitioned into two equal halves by a fixed diathermic separator. Two different ideal gases are filled in the left $(L)$ and right $(R)$ halves. The rms speed of the molecules in the $L$ part is equal to the mean speed of the molecules in the $R$ part. Then the ratio of the mass of a molecule in the $L$ part to that of a molecule in the $R$ part is

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

Similar Questions

For a mixture of three different gases with molecular masses $m_1 > m_2 > m_3$ at the same temperature,what is the relationship between their root mean square speeds $(v_{rms})$ and average kinetic energies $(\bar{K})$?

The speeds of $5$ gas molecules are $2, 3, 4, 5,$ and $6$ units respectively. What is the $rms$ speed of these molecules?

The $rms$ speed of gas molecules in a container is $400 \, ms^{-1}$. If half of the gas is removed at a constant temperature,the new $rms$ speed will be .... $ms^{-1}$.

The respective speeds of five molecules are $2, 1.5, 1.6, 1.6$ and $1.2 \, km/s$. The most probable speed in $km/s$ is:

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