Distribution of Speeds of Gas Molecules

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

In Maxwell-Boltzmann distribution, the fraction of gas molecules having energy between $\mathrm{E}$ and $\mathrm{E}+\mathrm{dE}$ is proportional to

The mean free path and RMS velocity of a nitrogen molecule at a temperature $17 °\mathrm{C}$ are $1.2\times {10}^{-7}$ $\mathrm{m}$ and $5\times {10}^2 \mathrm{m} {\mathrm{s}}^{-1}$, respectively. The mean time between two successive collisions will be $x\times {10}^{-11} \mathrm{s}$, what is the value of $x$.

The mean free path of molecules of a gas (radius ‘$r$’) is inversely proportional to $r^2$.

Assertion: Consider a system of gas having N molecules; Instantaneous K.E. of few molecules can be greater than average K.E. of the molecules of the given gas.

Reason: Number of molecules having most probable speed is greater than number of molecules having average speed.

The mean free path $\left(\mathrm{\lambda }\right)$ of a gas sample is given by:

If the temperature and pressure of a gas is doubled the mean free path of the gas molecules

Which of the following statement is wrong about Maxwell's distribution curve?

What happens when the gas becomes hotter?

How can we find the most probable speed of molecules using maxwell's distribution curve for velocities of molecules of a gas?

Area under maxwell distribution represents the number of number of molecules per unit volume.

For a molecule of an ideal gas, the number density is $2\sqrt{2}\times {10}^8 {\mathrm{cm}}^{-3}$ and the mean free path is $\frac{{10}^{-2}}{\pi } \mathrm{cm}$. The diameter of the gas molecule is

Explain Maxwell distribution of molecular speeds with necessary graph. 

Define the following 

Mean free path

Define the following

Free path

The expression $n\left(r\right)=n_0{e}^{-\alpha x^4}$ represents the number density of molecules of a gas as a function of distance$r$ from the origin. If it is known that the total number of molecules is proportional to $n_0{\alpha }^{-\mathrm{P}}$, then find the value of $\mathrm{P}$.

Assertion: The root mean square velocity of molecules of a gas having Maxwellian distribution of velocities is higher than their most probable velocity, at any temperature.

Reason: A very small number of molecules of a gas which possess very large velocities, increase the root mean square velocity, without affecting the most probable velocity.

In the following a statement of Assertion is followed by a statement of Reason.

Assertion: Mean free path of a gas molecule is inversely proportional to the density of gas.

Reason: Path of a gas molecule between two adjacent collision is straight line.

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^q$ , where $V$ is the volume of the gas. The value of $q$ is $\left(\mathrm{\gamma }=\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{v}}}\right)$

Assertion: Maxwell speed distribution graph is symmetric about most probable speed.

Reason: rms speed of ideal gas, depends upon its type (monoatomic, diatomic and polyatomic)