I E Irodov Solutions for Chapter: THERMODYNAMICS AND MOLECULAR PHYSICS, Exercise 3: KINETIC THEORY OF GASES, BOLTZMANN' S LAW AND MAXWELL'S DISTRIBUTION

Find the number of degrees of freedom of molecules in a gas, whose molar heat capacity
$\left(\mathrm{a}\right)$ at constant pressure, is equal to $C_p=29 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$,
$\left(\mathrm{b}\right)$ is equal to $C=29 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$, in the process, $pT=$constant.

Find the adiabatic exponent $\gamma$, for a mixture consisting of $v_1$ moles of a monatomic gas and $v_2$ moles of a gas of rigid diatomic molecules.

A thermally insulated vessel, with gaseous nitrogen, at a temperature $T= 27 °\mathrm{C}$, moves with velocity $v=100 \mathrm{m} {\mathrm{s}}^{-1}$. How much (in per cent) and in what way will the gas pressure change, on a sudden stoppage of the vessel?

Calculate, at the temperature, $T=17 °\mathrm{C}$,
$\left(\mathrm{a}\right)$ the root mean square velocity and the mean kinetic energy of an oxygen molecule, in the process of translational motion,
$\left(\mathrm{b}\right)$ the root mean square velocity of a water droplet, of diameter $d=0.10 \mathrm{\mu m}$, suspended in the air. 

A gas, consisting of rigid diatomic molecules, is expanded adiabatically. How many times has the gas to be expanded, to reduce the root mean square velocity of the molecules, $\eta = 1.50$ times?

The mass $m=15 \mathrm{g}$, of nitrogen, is enclosed in a vessel, at a temperature $T=300 \mathrm{K}$. What amount of heat has to be transferred to the gas, to increase the root mean square velocity of its molecules, $\eta =2.0$ times? 

The temperature of a gas, consisting of rigid diatomic molecules, is $T=300 \mathrm{K}$. Calculate the angular root mean square velocity of a rotating molecule, if its moment of inertia is equal to $I=$ $2.1\times {10}^{-39} \mathrm{g} {\mathrm{cm}}^2$.

A gas consisting of rigid diatomic molecules, was initially under standard conditions. Then the gas was compressed adiabatically $\eta =5.0$ times. Find the mean kinetic energy of a rotating molecule in the final state.