If the collision frequency of hydrogen molecu | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The collision frequency $Z$ of gas molecules is given by the relation $Z \propto n \sigma v_{avg}$,where $n$ is the number density,$\sigma$ is the

Vedclass · Accepted Answer

$\frac{2}{\sqrt{3}} Z$

Vedclass · Answer

(C) The collision frequency $Z$ of gas molecules is given by the relation $Z \propto n \sigma v_{avg}$,where $n$ is the number density,$\sigma$ is the collision cross-section,and $v_{avg}$ is the average speed.In a closed chamber,the number density $n$ and the collision cross-section $\sigma$ remain constant.The average speed $v_{avg}$ is proportional to the square root of the absolute temperature,i.e.,$v_{avg} \propto \sqrt{T}$.Therefore,the collision frequency $Z \propto \sqrt{T}$.Given,$T_1 = 27^{\circ} C = 300 \ K$ and $T_2 = 127^{\circ} C = 400 \ K$.Using the ratio: $\frac{Z_2}{Z_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{400}{300}} = \sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}$.Thus,$Z_2 = \frac{2}{\sqrt{3}} Z$.

If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ} C$ is $Z$,then the collision frequency of the same system at $127^{\circ} C$ is :

Similar Questions

Assertion $(A):$ The total translational kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its pressure and volume.
Reason $(R):$ The molecules of gas collide with each other and the velocities of the molecules change due to the collision.

$N$ moles of a diatomic gas in a cylinder are at a temperature $T$. Heat is supplied to the cylinder such that the temperature remains constant but $n$ moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas?

$A$ molecule in a gas container hits a horizontal wall with speed $200 \; m s^{-1}$ at an angle of $30^{\circ}$ with the normal,and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?

At a temperature of $300 \ K$,the average translational kinetic energy and $rms$ speed of a sample of oxygen gas are $6.21 \times 10^{-21} \ J$ and $484 \ m/s$ respectively. At $600 \ K$,these values will be respectively: (Assume ideal gas behavior)

Which one of the following gases possesses the largest internal energy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module