B M Sharma Solutions for Chapter: Kinetic Theory of Gases, Exercise 1: ILLUSTRATIONS

The highest vacuum attained so far is of the order of ${10}^{-11} \mathrm{mm}$ of mercury. How many molecules are there in $1 \mathrm{cc}$ of a vessel under such a high vacuum at $0°\mathrm{C}$ ?

A closed container of volume $0.02{ \mathrm{m}}^3$ contains a mixture of neon and argon gases at $27°\mathrm{C}$ temperature and $1.0\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$ pressure. The gram-molecular weights of neon and argon are $20$ and $40$, respectively. Find the masses of the individual gases in the container. Assuming them to be ideal $\left(R=8.314 \mathrm{J}/\mathrm{mol}-\mathrm{K}\right)$. Total mass of the mixture is $28 \mathrm{g}$.

A glass container encloses a gas at a pressure of $8\times {10}^5 \mathrm{Pa}$ and $300 \mathrm{K}$ temperature. The container walls can bear a maximum pressure of ${10}^6 \mathrm{Pa}$. If the temperature of container is gradually increased, find the temperature at which the container will break.

Calculate the number of molecules in $1 \mathrm{cc}$ of an ideal gas at $27°\mathrm{C}$ and a pressure of $10 \mathrm{mm}$ of mercury. Mean kinetic energy of molecule at $27°\mathrm{C}$ is $4\times {10}^{-14} \mathrm{erg}$; the density of mercury is $13.6 \mathrm{g}/\mathrm{cc}$.

A spherical balloon of volume $\mathrm{V}$ contains helium at a pressure $\mathrm{P}$. How many moles of helium are in the balloon if the average kinetic energy of the helium atoms is $\overline{\mathrm{K}}$?

A $5.00 \mathrm{L}$ vessel contains nitrogen gas at $27.0°\mathrm{C}$ and $3.00 \mathrm{atm}$. Find

(a) the total translational kinetic energy of the gas molecules and

(b) the average kinetic energy per molecule. [Take $\mathrm{atm}$. pressure $=1.0\times {10}^5 \mathrm{Pa}$ and ${\mathrm{N}}_{\mathrm{A}}=6.0\times {10}^{23}$]

A $7.00 \mathrm{L}$ vessel contains $3.5$ moles of gas at a pressure of $1.66\times {10}^6 \mathrm{Pa}$. Find

(a) the temperature of the gas;

(b) the average kinetic energy of the gas molecules in the vessel.

(c) What additional information would you need if you were asked to find the average speed of the gas molecules? $\left(R=8.3 \mathrm{J}/\mathrm{mol}-\mathrm{K}, \overline{K}=1.38\times {10}^{-23} \mathrm{J} {\mathrm{K}}^{-1}\right)$

A spherical balloon of volume $4.00 \times 10^{3} \mathrm{~cm}^{3}$ contains helium at a pressure of $1.20 \times 10^{5} \mathrm{~Pa}$. How many moles of helium are in the balloon if the average kinetic energy of the helium atoms is $3.60 \times 10^{-22} \mathrm{~J} ?$