Kinetic Theory

A flask contains argon and chlorine in the ratio of 2 : 1 by mass. The Temperature of the mixture is \(27^\circ C\). The ratio of root mean square speed of the molecules of the two gases \(\left(\frac{{v}_{rms}^{Ar}}{{v}_{rms}^{Cl}}\right)\) is :
(Atomic mass of argon \(=40.0\mathrm{u}\) and molecular mass of chlorine = 70.0 u )

A container has two chambers of volumes \({\mathrm{V}}_{1}=2\) litres and \({\mathrm{V}}_{2}=3\) litres separated by a partition made of a thermal insulator. The chambers contains \({\mathrm{n}}_{1}=5\) and \({\mathrm{n}}_{2}=4\) moles of ideal gas at pressures \({\mathrm{p}}_{1}=1\mathrm{atm}\) and \({\mathrm{p}}_{2}=2\mathrm{atm}\), respectively. When the partition is removed, the mixture attains an equilibrium presšure of :

[NEET 2025]

An oxygen cylinder of volume \(30\) litre has \(18.20\) moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to \(11\) atmospheric pressure at temperature \(27^\circ \mathrm{C}\). The mass of the oxygen withdrawn from the cylinder is nearly equal to:
[Given, \(\mathrm{R}=\frac{100}{12}\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}\), and molecular mass of \({\mathrm{O}}_{2}=32\), 1 atm pressure \(=1.01\times {10}^{5}\mathrm{N}/\mathrm{m}\)]

[NEET 2025]

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:

[JEE Main 2023, 25 Jan (Shift 2)]

Given below are two statements:
Statements I: The temperature of a gas is \(-73^{\circ} C\). When the gas is heated to \(527^{\circ} C\), the root mean square speed of the molecules is doubled.

Statement II: The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.

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

If the rms speed of oxygen molecules at \(0^{\circ} C\) is \(160 m / s\), find the rms speed of hydrogen molecules at \(0^{\circ} C\).

[JEE Main 2021, 27 Aug (Shift 2)]

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at \(27^{\circ} C\) is

[JEE Main 2023, 8 Apr (Shift 2)]

A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas \((\gamma=5 / 3)\) and one mole of an ideal diatomic gas \((\gamma=7 / 5)\). Here, \(\gamma\) is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of 66 Joule when heated at constant pressure. The change in its internal energy is ________ Joule.

[JEE Advanced 2023]

An ideal gas equation can be written as; \(\mathrm{P}=\frac{\rho \mathrm{RT}}{{\mathrm{M}}_{0}}\),where \( \rho \) and \( \mathrm{M}_{0} \) are respectively,

A balloon carries a total load of \(185 kg\) at normal pressure and temperature of \(27^{\circ} C\). What load with the balloon carry on rising to a height at which the barometer pressure is 45 \(cm\) of \(Hg\) and the temperature –7°C. Assuming the volume constant.

The temperature of a gas is \(-50^\circ \mathrm{C}\). To what temperature the gas should be heated so that the rms speed is increased by 3 times?

[NEET 2023]

Given below are two statements:
Statement I: The temperature of a gas is \(-73^{\circ} C\). When the gas is heated to \(527^{\circ} C\), the root mean square speed of the molecules is doubled.

Statement II: The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.

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

Consider a sample of oxygen behaving like an ideal gas. At \(300 K\), the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be:
(Molecular weight of oxygen is \(32 g / mol ; R=8.3 JK ^{-1}\) \(\left.mol ^{-1}\right)\)

The average thermal energy for a mono-atomic gas is : (k_B is Boltzmann constant and \( \mathrm{T} \), absolute temperature)

[NEET 2020]

The number of air molecules per \(cm ^3\) increased from \(3 \times 10^{19}\) to \(12 \times 10^{19}\). The ratio of collision frequency of air molecules before and after the increase in number respectively is

The mean free path for a gas, with molecular diameter d and number density n can be expressed as :

[NEET 2020]

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed \(\left(V_{r m s}\right)\) and choose the correct answer from the options given below:

[JEE Main 2023, 11 Apr (Shift 1)]

A cylinder contains hydrogen gas at pressure of \( 249 \mathrm{kPa} \) and temperature \( 27^{\circ} \mathrm{C} \). Its density is \( :\left(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right) \)

[NEET 2020]