Kinetic Theory

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are 3 × 10⁻⁷ m and 600 m/s, respectively. Find the frequency of its collisions.

Nitrogen has is at 300° temperature. The temperature (in K) at which the rms speed of a H? molecule would be equal to the rms speed of a nitrogen molecule, is (Molar mass of N? gas 28 g)

The plot that depicts the behavior of the mean free time $\tau$ $$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature $\left(T\right)$ $$ , qualitatively, is: (Graphs are schematic and not drawn to scale)

Calculate the value of mean free path (λ) for oxygen molecules at temperature 27° C and pressure 1.01×10⁵ Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 x 10⁻²³ JK⁻¹)

The number of molecules in one litre of an ideal gas at 300K and 2 atmospheric pressure with mean kinetic energy 2 × 10? J per molecule is:
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The root mean  square speed of molecules of a given mass of a gas at 27°C and 1 atmosphere pressure is 20 ms^-1. The root mean square speed of molecules of the gas at 127°C and 2 atmosphere pressure is $\frac{x}{\sqrt[]{3}}m{s}^{-1}.$ <!-- [if gte mso 9]><xml> </xml><![endif]--> The value of x will be………………….

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

A mono-atomic gas of mass 4.0u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R = gas constant) is $\frac{x}{3R}.$ <!-- [if gte mso 9]><xml> </xml><![endif]--> Value of x is…………….

Given below are two statements:                                        

Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell’s distribution.

Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.

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

The following graph represents the $T-V$ curves of an ideal gas (where $T$ is the temperature and $V$ the volume) at three pressures $P_1,P_2$ and $P_3$  compared with those of Charles's law represented as dotted lines.