Embibe Experts Solutions for Chapter: Kinetic Theory of Gases, Exercise 2: Level 2

Initially a gas of diatomic molecules is contained in a cylinder of volume $V_1$ at a pressure $P_1$ and temperature $250 \mathrm{K}.$ Assuming that $25\%$ of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature $2000 \mathrm{K},$ when contained in a volume $2 {\mathrm{V}}_1$is given by $P_2.$ The ratio $\frac{P_2}{P_1}$ is_____.

The average translational energy and the rms (root mean square) speed of molecules in a sample of oxygen at $300 \mathrm{K}$ are $6.21\times {10}^{-21} \mathrm{J}$ and $484 \mathrm{m} {\mathrm{s}}^{-1}$ respectively. The corresponding values at $600 \mathrm{K}$ are nearly (assuming ideal gas behaviour).
 

If $V_H, V_N$ and $V_0$ denotes the root mean square velocity of molecules of Hydrogen, Nitrogen and Oxygen respectively at a given temperature then.

An ideal gas filled in a cylinder occupies volume $V$. The gas is compressed isothermally to the volume $\frac{V}{3}$. Now the cylinder valve is opened and the gas is allowed to leak keeping temperature same. What percentage of the number of molecules escape to bring the pressure in the cylinder back to its original value.

A jar has a mixture of hydrogen and oxygen gas in the ratio of $1:5$. The ratio of mean kinetic energies of hydrogen and oxygen molecules is

The average kinetic energy of molecules are 

In the nuclear fusion reaction  ${}_1{}^2\mathrm{H}+{}_1{}^3\mathrm{H}\stackrel{}{\to }{}_2{}^4\mathrm{He}+\mathrm{n}$. It is given that the repulsive potential energy between the two nuclei is $~7.7\times {10}^{-14} \mathrm{J}$, the temperature at which the gases must be heated to initiate the reaction is nearly $[$Boltzmann's constant $\left.\mathrm{k}=1.38\times {10}^{-23} \mathrm{J} {\mathrm{K}}^{-1}\right]$

Pressure of a gas increases due to increase of its temperature because at higher temperature