Embibe Experts Solutions for Chapter: Kinetic Theory of Gases, Exercise 1: AP EAPCET 2019 (21-Apr Shift-2)

A diatomic gas consisting of rigid molecules is at a temperature of $87 °\mathrm{C}$. If the moment of inertia of the rotating diatomic rigid molecule is $2.76\times {10}^{-39} \mathrm{g} {\mathrm{cm}}^2$, then the rms angular speed of the molecule is $($Boltzmann constant $=1.38\times {10}^{-23} \mathrm{J} {\mathrm{K}}^{-1}$)

When the temperature of an ideal gas is increased from $27°\mathrm{C}$ to $127°\mathrm{C}$, calculate the percentage increase in its ${\mathrm{v}}_{rms}$.

For a gas the value of $\frac{R}{C_v}=0.4,$ so the gas is
(R-Universal gas constant)

A diatomic gas is heated at constant pressure, what fraction of the heat energy is used to increase the internal energy?

Tyre of a bicycle has volume $2\times {10}^{-3} {\mathrm{m}}^3$. Initially the tube is filled $75\%$ of its volume by air at atmospheric pressure ${10}^5 \mathrm{N} {\mathrm{m}}^{-2}$. When a rider is on the bicycle, the area of contact of tyre with road is $24\times {10}^{-4} {\mathrm{m}}^2$. The mass of rider with bicycle is $120 \mathrm{kg}$. If a pump delivers a volume $500 {\mathrm{cm}}^3$ of air in each stroke then the number of strokes required to inflate the tyre is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A balloon contains $1500{ \mathrm{m}}^3$ of $\mathrm{He}$ at $27°\mathrm{C}$ and $4$ atmospheric pressure. the volume of $\mathrm{He}$ at $-3°\mathrm{C}$ temperature and $2$ atmospheric pressure will be

A vessel has $6 \mathrm{g}$ of oxygen at pressure $P$ and temperature $400 \mathrm{K}$. A small hole is made in it so that oxygen leaks out. How much oxygen leaks out if the final pressure is $\frac{P}{2}$ and temperature is $300 \mathrm{K}$?

The pressure of a gas is proportional to