# Root Mean Square Speed

## Trending Questions

**Q.**For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127∘C. At 2 atm pressure and at 227∘C, the rms speed of the molecules will be

- 100√5 m/s
- 80 m/s
- 100 m/s
- 80√5 m/s

**Q.**

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

$1:2:3$

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

$\sqrt{2}:\sqrt{3}:\sqrt{8\mathrm{\xcf\u20ac}}$

$\sqrt{2}:\sqrt{\raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\xcf\u20ac}$}\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?

- Average kinetic energy per molecule of A is equal to that of B.
- Root-mean-square value of translational velocity of B is four times that of A.
- Pressure exerted by B is eight times of that exerted by A.
- 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

- 2V
- V
- 4V
- √2V

**Q.**

The average kinetic energy of a gas molecule at 27∘ is 6.21×10−21J. The average kinetic energy at 227∘ will be

9.35×10−21J

10.35×10−21J

11.35×10−21J

12.35×10−21J

**Q.**The root mean square speed of the molecules of a gas is 1260 m/s. The average speed of the molecules is

- 1061 m/s
- 1260 m/s
- 1161 m/s
- 1671 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 $\mathrm{dU}:\mathrm{dQ}:\mathrm{dW}$

.$3:7:2$

$5:7:2$

$5:7:3$

$3:5:2$

**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 S.T.P, keeping pressure constant?

- 819∘C
- 1012∘C
- 273∘C
- 514∘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

- 2v
- 4v
- v
- v√2

**Q.**The temperature of an ideal gas is increased from 27∘C to 127∘C. Then, percentage increase in Vrms is

- 37%
- 11%
- 33%
- 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 K are 6.21×10−21 J and 484 m/s respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour)

- 2.42×10−20 J and 968 m/s
- 8.78×10−20 J and 684 m/s
- 6.21×10−20 J and 968 m/s
- 1.24×10−20 J and 684 m/s

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

- 300 m/s
- 150 m/s
- 600 m/s
- 175 m/s

**Q.**The rms speed of oxygen at room temperature is about 500 m/s. The rms speed of hydrogen at the same temperature is about

- 125 m/s
- 2000 m/s
- 8000 m/s
- 31 m/s

**Q.**The rms velocity of gas molecules of a given amount of a gas at 27∘C and 1.0×105N m−2 pressure is 200 m sec−1. If temperature and pressure are respectively 127∘C and 0.5×105 N m−2, the rms velocity will be:

- 400√3 ms−1
- 100√2 ms−1
- 100√23 ms−1
- 50√23 ms−1

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

- Hydrogen
- Nitrogen
- Oxygen
- Carbon dioxide

**Q.**

Nitrogen gas is at temperature$300\xc2\xb0C$. 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 ?

- r2
- r−2
- r−3
- r−4

**Q.**

The kinetic energy of molecules is directly proportional to:

Temperature

Pressure

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?

$40\mathrm{g}$

$55\mathrm{g}$

$32\mathrm{g}$

$44\mathrm{g}$

**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 v2 and the mean square of x component of the velocity of moleccules of gas A is w2. The ratio w2v2 is

- 1
- 2
- 13
- 23

**Q.**The root mean square speed of molecules of a given mass of a gas at 27° C and 1 atmosphere pressure is 200 ms−1. The root mean square speed of molecules of the gas at 127° C and 2 atmosphere pressure is x√3 ms−1

. The value of x will be

**Q.**The root mean square speed of the molecules of a gas is 1260 m/s. The average speed of the molecules is

- 1260 m/s
- 1161 m/s
- 1671 m/s
- 1061 m/s

**Q.**

If the temperature of a gas is increased from 27∘ C to 927∘C, the root mean square speed of its molecules

is doubled

remains unchanged

becomes 4 times

becomes half

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

- 8.5 v
- 7.5 v
- 9.5 v
- 6.5 v

**Q.**Given Avagadro number = 6.02×1023 and Boltzmann's constant =1.38×10−23 J/(mol.-K). Calculate (a) the average kinetic energy of translation of an oxygen molecule at 27∘C, (b) the total average kinetic energy of an oxygen molecule at 27∘C, (c) the total kinetic energy in Joules of a gram-molecule of oxygen at 27∘C.

- joule/molecule , 600 joule/molecule.
- joule/molecule , 298 joule/molecule.
- joule/molecule , 6231 joule/molecule.
- 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∘C?

273∘C

1219∘C

200∘C

1492∘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 ¯vH will be related to helium ¯vHe as

- ¯vH=¯vHe
- ¯vH=¯vHe2
- ¯vH=√2¯vHe
- ¯vH=2¯vHe

**Q.**Suppose a container is evacuated to leave just one molecule of a gas in it. Let vav and vrms represent the average speed and rms speed of the gas.

- vav>vrms
- vav<vrms
- vav=vrms
- vrms is undefined