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

Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases which obey the Maxwellian's distribution of velocities. Vessel $A$ contains only ${\mathrm{O}}_2, B$ only ${\mathrm{N}}_2$ and $C$ a mixture of equal quantities of ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$. If the average speed of the ${\mathrm{O}}_2$ molecules in vessel $A$ is $v_1,$ that of the ${\mathrm{N}}_2$ molecules in vessel $B$ is $v_2$, the average speed of the ${\mathrm{O}}_2$ molecules in vessel $C$ is (where $M$ is the mass of an oxygen molecule)

When a gas is heated in a vessel of constant volume, the pressure increases because

Pressure versus temperature graph of an ideal gas is shown in figure. Density of the gas at point $A$ is ${\rho }_0$. Density at $B$ will be:-

A vessel is partitioned in two equal halves by a fixed diathermic separator. Two different ideal gases are filled in left $\left(L\right)$ and right $\left(R\right)$ halves. The root-mean-square speed of the molecules in $L$ part is equal to the mean speed of molecules in the $R$ part. Then the ratio of the mass of a molecule in $L$ part to that of a molecule in $R$  part is:-

A closed vessel contains a mixture of two diatomic gases $A$ and $B$. Molar mass of $A$ is $16$ times that of $B$ and mass of gas $A$ contained in the vessel is $2$ times that of $B$. Choose the correct statement($\mathrm{s}$).

Let   $\overline{v}$,  $v_{\mathrm{rms}}$ and $v_{\mathrm{p}}$  respectively denote the mean speed, root-mean-square speed and most probable speed of the molecules in an ideal mono atomic gas at absolute temperature  $\mathrm{T}$. The mass of a molecule is  $\mathrm{m}$. Then,

The pressure of one mole of an ideal gas varies according to the law $P=P_0-a{V}^2$, where $P_0$ and a are positive constants. The highest temperature that the gas may attain is:-

Graph shows a hypothetical speed distribution for a sample of $N$ gas particle:( for $V>V_0;\frac{dN}{dV}=0$ )