B M Sharma Solutions for Chapter: Kinetic Theory Of Gases, Exercise 1: DPP

The $\mathrm{RMS}$ speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at $0 °\mathrm{C}$ is $3180 \mathrm{m} {\mathrm{s}}^{-1}.$ The pressure on the hydrogen gas is _____ $\mathrm{atm}$(density of hydrogen gas is $8.99\times {10}^{-2} \mathrm{kg} {\mathrm{m}}^{-3},$ $1 \mathrm{atm}=1.01\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$)

A cylinder of capacity $20 \mathrm{L}$ is filled with ${\mathrm{H}}_2$ gas. The total average kinetic energy of translatory motion of its molecules is $1.5\times {10}^5 \mathrm{J}$. The pressure of hydrogen in the cylinder is $5\times$${10}^{\mathrm{x}}$ $\mathrm{N} {\mathrm{m}}^{-2}$. The value of $\mathrm{x}$ is _____.

A flask contains ${10}^{-3} {\mathrm{m}}^3$ gas. At temperature, the number of molecules of oxygen is $3.0\times {10}^{22}$. The mass of an oxygen molecule is $5.3\times {10}^{-26} \mathrm{kg}$ and at that temperature the RMS velocity of molecules is  $400 \mathrm{m} {\mathrm{s}}^{-1}$. The pressure in $\mathrm{N} {\mathrm{m}}^{-2}$ of the gas in the flask is $\mathrm{y}\times {10}^4 \mathrm{N} {\mathrm{m}}^{-2}$. The value of $\mathrm{y}$ is _____. 

When the volume of the system is increased _____ times and the temperature is decreased half of its initial temperature, then pressure becomes one-fourth.

Let $\mathrm{A}$ and $\mathrm{B}$ the two gases and given $\frac{T_{\mathrm{A}}}{M_{\mathrm{A}}}=4\frac{T_{\mathrm{B}}}{M_{\mathrm{B}}}$, where $T$ is the temperature and $M$ is the molecular mass. If $C_A$ and $C_B$ are the $\mathrm{RMS}$ speeds, then the ratio $\frac{C_{\mathrm{A}}}{C_{\mathrm{B}}}$ will be equal to _____.

The $\mathrm{RMS}$ speed of the molecules of a gas in a vessel is $400 \mathrm{m} {\mathrm{s}}^{-1}$. If half of the gas leaks out at a constant temperature, the $\mathrm{RMS}$ speed of the remaining molecules will be _____$\mathrm{m} {\mathrm{s}}^{-1}$.

The root mean square speed of hydrogen molecules at $300 \mathrm{K}$ is $1930 \mathrm{m} {\mathrm{s}}^{-1}$. Then the root mean square speed of oxygen molecules at $900 \mathrm{K}$ will be _____ $\mathrm{m} {\mathrm{s}}^{-1}$.

The speeds of $5$ molecules of a gas (in arbitrary $\mathrm{units}$) are as follows: $2$, $3$, $4$, $5$ and $6$. The root mean square speed for these molecules is _____ $\mathrm{units}$.