Molecular speeds

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: If the average kinetic energy of $\ce{H2}$ and $\ce{O2}$ molecules, kept in two different sized containers are same, then their temperatures will be same.

Reason R: The r.m.s. speed of $\ce{H2}$ and $\ce{O2}$ molecules are same at same temperature.

Choose the correct answer from the options given below

0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127°C. The amount of heat required to double the speed of its molecules is ______ k cal.

(Take $R=2$ cal mole$^{-1}$K$^{-1}$)

The relation between root mean square speed ($v_{\rm rms}$) and most probable speed ($v_p$) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen ?

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is 1:4, then

A. The r.m.s. velocity of gas molecules in two vessels will be the same.

B. The ratio of pressure in these vessels will be 1:4.

C. The ratio of pressure will be 1:1.

D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of 1:4.

Choose the correct answer from the options given below :

Given below are two statements :

Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.

Statement II : 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 $2v$.

In the light of the above statements, choose the correct answer from the options given below :

A vessel contains 14 g of nitrogen gas at a temperature of 27°C. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be :

Take R = 8.32 J mol$^{-1}$ k$^{-1}$.

The root mean square speed of smoke particles of mass $5\times10^{-17}$ kg in their Brownian motion in air at NTP is approximately. [Given k = $1.38\times10^{-23}$ J K$^{-1}$]

If the r.m.s speed of oxygen at room temperature is $\sqrt{56}$ m/s. The r.m.s speed of nitrogen at the same temperature is _______.

A flat plate is moving normal to its plane through a gas under the action of a constant force $F$. The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature $T$. Assuming the gases are ideal, the correct statement(s) is(are)

At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 ms$^{-1}$. The gas is :

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 $\left(\dfrac{v_{rms}(\text{helium})}{v_{rms}(\text{argon})}\right)$ is