Root Mean Square Speed

Q. For a given gas at $1\text{atm}$ pressure, $rms$ speed of the molecules is $200\text{m/s}$ at ${127}^{\circ }\text{C}$. At $2\text{atm}$ pressure and at ${227}^{\circ }\text{C}$, the $rms$ speed of the molecules will be

1. $100\sqrt{5}\text{m/s}$
2. $80\text{m/s}$
3. $100\text{m/s}$
4. $80\sqrt{5}\text{m/s}$

Q.

The ratio among most probable velocity, mean velocity, and root mean square velocity is given by:

1. $1:2:3$

2. $1:\sqrt{2}:\sqrt{3}$

3. $\sqrt{2}:\sqrt{3}:\sqrt{8\pi }$

4. $\sqrt{2}:\sqrt{\raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$\pi $}\right.}:\sqrt{3}$

Q. A certain gas takes three times as long to effuse out as helium. Its molecular mass will be

Q. A closed vessel contains a mixture of two diatomic gases $A$ and $B$. Molar mass of $A$ is 16 times that of $B$ and mass of gas $A$ contained in the vessel is 2 times that of $B$. Which of the following statements are correct?

1. Average kinetic energy per molecule of $A$ is equal to that of $B$.
2. Root-mean-square value of translational velocity of $B$ is four times that of $A$.
3. Pressure exerted by $B$ is eight times of that exerted by $A$.
4. Number of molecules of $B$, in the cylinder, is eight times that of $A$.

Q. The rms speed of oxygen molecules in a gas is $V$. If the temperature is doubled and oxygen molecules dissociate into oxygen atoms, the rms speed will become

1. $2V$
2. $V$
3. $4V$
4. $\sqrt{2}V$

Q.

The average kinetic energy of a gas molecule at ${27}^{\circ }$ is $6.21\times {10}^{-21}J.$ The average kinetic energy at ${227}^{\circ }$ will be

1. $9.35\times {10}^{-21}J$
   

2. $10.35\times {10}^{-21}J$
   

3. $11.35\times {10}^{-21}J$
   

4. $12.35\times {10}^{-21}J$

Q. The root mean square speed of the molecules of a gas is $1260\text{m/s}$. The average speed of the molecules is

1. $1061\text{m/s}$
2. $1260\text{m/s}$
3. $1161\text{m/s}$
4. $1671\text{m/s}$

Q.

A diatomic gas, having ${\mathrm{C}}_{\mathrm{P}}=(7/2)\mathrm{R}$ and ${\mathrm{C}}_{\mathrm{v}}=(5/2)\mathrm{R},$ is heated at constant pressure. The ratio $\mathrm{dU}:\mathrm{dQ}:\mathrm{dW}$

1. .$3:7:2$

2. $5:7:2$

3. $5:7:3$

4. $3:5:2$

Q.

The root mean square (R.M.S.) Speed V of the molecules of an ideal gas is given by the expressions, $\mathrm{v}=\sqrt{\left(\frac{3\mathrm{RT}}{\mathrm{M}}\right)}$ and $\mathrm{v}=\sqrt{\left(\frac{3\mathrm{KT}}{\text{m}}\right)}$ where R is universal gas constant, T is the absolute (Kelvin) temperature M is the molar mass, K is Boltzmans constant and m is the molecular mass. The R.M.S. speed of oxygen molecules (${\mathrm{O}}_2$) at temperature ${\mathrm{T}}_1\mathrm{is}{\mathrm{V}}_1$. When the temperature is doubled, if the oxygen molecules are dissociated into atomic oxygen, what will be R.M.S. speed of oxygen atoms? (Treat the gas as ideal).

Q. At what temperature root mean square velocity of hydrogen becomes double of its value at $\text{S.T.P}$, keeping pressure constant?

1. ${819}^{\circ }\text{C}$
2. ${1012}^{\circ }\text{C}$
3. ${273}^{\circ }\text{C}$
4. ${514}^{\circ }\text{C}$

Q. The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become

1. $2v$
2. $4v$
3. $v$
4. $v\sqrt{2}$

Q. The temperature of an ideal gas is increased from ${27}^{\circ }\text{C}$ to ${127}^{\circ }\text{C}$. Then, percentage increase in $V_{rms}$ is

1. $37\%$
2. $11\%$
3. $33\%$
4. $15.5\%$

Q. The average translational kinetic energy and the root mean square speed of the molecules in a sample of oxygen gas at $300\text{K}$ are $6.21\times {10}^{-21}\text{J}$ and $484\text{m/s}$ respectively. The corresponding values at $600\text{K}$ are nearly (assuming ideal gas behaviour)

1. $2.42\times {10}^{-20}\text{J}$ and $968\text{m/s}$
2. $8.78\times {10}^{-20}\text{J}$ and $684\text{m/s}$
3. $6.21\times {10}^{-20}\text{J}$ and $968\text{m/s}$
4. $1.24\times {10}^{-20}\text{J}$ and $684\text{m/s}$

Q. The root mean square speed of a gas molecule is $300\text{m/s}$. What will be the root mean square speed of the molecules if the atomic mass is doubled and absolute temperature is halved?

1. $300\text{m/s}$
2. $150\text{m/s}$
3. $600\text{m/s}$
4. $175\text{m/s}$

Q. The rms speed of oxygen at room temperature is about $500\text{m/s}$. The rms speed of hydrogen at the same temperature is about

1. $125\text{m/s}$
2. $2000\text{m/s}$
3. $8000\text{m/s}$
4. $31\text{m/s}$

Q. The rms velocity of gas molecules of a given amount of a gas at ${27}^{\circ }\text{C}$ and $1.0\times {10}^5{\text{N m}}^{-2}$ pressure is $200{\text{m sec}}^{-1}$. If temperature and pressure are respectively ${127}^{\circ }\text{C}$ and $0.5\times {10}^5{\text{N m}}^{-2}$, the rms velocity will be:

1. $\frac{400}{\sqrt{3}}{\text{ms}}^{-1}$
2. $100\sqrt{2}{\text{ms}}^{-1}$
3. $100\frac{\sqrt{2}}{3}{\text{ms}}^{-1}$
4. $50\sqrt{\frac{2}{3}}{\text{ms}}^{-1}$

Q. Which of the following gases has maximum rms speed at a given temperature?

1. Hydrogen
2. Nitrogen
3. Oxygen
4. Carbon dioxide

Q.

Nitrogen gas is at temperature$300°C$. The temperature (in $K$) at which the $rms$ speed of a $H_2$ molecule would be equal to the $rms$ speed of a nitrogen molecule is

Q. The force between two short dipoles separated by a distance r is directly proportional to ?

1. $r^2$
2. $r^{-2}$
3. $r^{-3}$
4. $r^{-4}$

Q.

The kinetic energy of molecules is directly proportional to:

1. Temperature

2. Pressure

3. Both a and b

Q.

What is the mass of carbon dioxide which contains the same number of molecules as are contained in $40\mathrm{g}$ of oxygen?

1. $40\mathrm{g}$

2. $55\mathrm{g}$

3. $32\mathrm{g}$

4. $44\mathrm{g}$

Q. $N$ molecules each of mass $m$ of gas A and $2N$ molecules each of mass $2m$ of gas B are contained in the same vessel at temperature T. The mean square of the velocity of molecules of gas B is $v^2$ and the mean square of x component of the velocity of moleccules of gas A is $w^2$. The ratio $\frac{w^2}{v^2}$ is

1. $1$
2. $2$
3. $\frac{1}{3}$
4. $\frac{2}{3}$

Q. The root mean square speed of molecules of a given mass of a gas at $27°\text{C}$ and $1$atmosphere pressure is $200{\text{ms}}^{-1}$. The root mean square speed of molecules of the gas at $127°\text{C}$ and $2$ atmosphere pressure is $\frac{x}{\sqrt{3}}{\text{ms}}^{-1}$
. The value of $x$ will be .

Q. The root mean square speed of the molecules of a gas is $1260\text{m/s}$. The average speed of the molecules is

1. $1260\text{m/s}$
2. $1161\text{m/s}$
3. $1671\text{m/s}$
4. $1061\text{m/s}$

Q.

If the temperature of a gas is increased from ${27}^{\circ }$ C to ${927}^{\circ }$C, the root mean square speed of its molecules

1. is doubled

2. remains unchanged

3. becomes 4 times
   

4. becomes half
   

Q. The velocities of three molecules are $3v,4v$ and $12v$ respectively. Their root mean square speed will be

1. $8.5v$
2. $7.5v$
3. $9.5v$
4. $6.5v$

Q. Given Avagadro number = $6.02\times {10}^{23}$ and Boltzmann's constant =$1.38\times {10}^{-23}$ J/(mol.-K). Calculate (a) the average kinetic energy of translation of an oxygen molecule at ${27}^{\circ }$C, (b) the total average kinetic energy of an oxygen molecule at ${27}^{\circ }$C, (c) the total kinetic energy in Joules of a gram-molecule of oxygen at ${27}^{\circ }$C.

1. joule/molecule , 600 joule/molecule.
2. joule/molecule , 298 joule/molecule.
3. joule/molecule , 6231 joule/molecule.
4. joule/molecule , 728 joule/molecule.

Q.

At what temperature would the root mean square speed of a gas molecule have twice its value at ${100}^{\circ }$C?

1. ${273}^{\circ }$C
   

2. ${1219}^{\circ }$C
   

3. ${200}^{\circ }$C
   

4. ${1492}^{\circ }$C

Q. In two vessels of same volume atomic hydrogen and helium at pressure $1$ atm and $2$ atm are filled. If temperature of both the samples is same, then average speed of hydrogen atom ${\overline{v}}_H$ will be related to helium ${\overline{v}}_{He}$ as

1. ${\overline{v}}_H={\overline{v}}_{He}$
2. ${\overline{v}}_H=\frac{{\overline{v}}_{He}}{2}$
3. ${\overline{v}}_H=\sqrt{2}{\overline{v}}_{He}$
4. ${\overline{v}}_H=2{\overline{v}}_{He}$

Q. Suppose a container is evacuated to leave just one molecule of a gas in it. Let $v_{av}$ and $v_{rms}$ ​ represent the average speed and rms speed of the gas.

1. $v_{av}>v_{rms}$
2. $v_{av}<v_{rms}$
3. $v_{av}=v_{rms}$
4. $v_{rms}$ is undefined