Kinetic theory of gases practice · Mixed difficulty

Find the loss in the mass of 1 mole of an ideal monatomic gas kept in a rigid container as it cools down by $10^{\circ} \mathrm{C}$. The gas constant $R=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$.

Mean kinetic energy (or average energy) per $g$ molecule of a monoatomic gas is given by

At the same temperature and pressure and volume of two gases, which of the following quantities is constant

If the volume of the gas containing $n$ number of molecules is $V,$ then the pressure will decrease due to force of intermolecular attraction in the proportion

The root mean square speeds of molecules of ideal gases at the same temperature are:

In Vander Wal's equation the critical pressure $P_c$ is given by

According to kinetic theory of gases,
A. The motion of the gas molecules freezes at $0^\circ C$
B. The mean free path of gas molecules decreases if the density of molecules is increased.
C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.
D. Average kinetic energy per molecule per degree of freedom is $\frac{3}{2}\,{k_B}T$ (for monoatomic gases).
Choose the most appropriate answer from the options given below:

Assertion: Each vibrational mode gives two degrees of freedom
Reason: By law of equipartition of energy, the energy for each degree of freedom in thermal equilibrium is $2 k_B T$

At what temperature the rms velocity of helium molecules will be equal to that of hydrogen molecules at NTP?

KE per unit volume is $E$. The pressure exerted by the gas is given by

The average thermal energy for a mono-atomic gas is: (${\mathrm{k}_\mathrm{B}}$ is Boltzmann constant and $\mathrm{T}$, absolute temperature)

The temperature at which the average translational kinetic energy of a molecule is equal to the energy gained by an electron in accelerating from rest through a potential difference of $1\;volt$ is

If a Vander-Waal’s gas expands freely, then final temperature is

For a gas molecule with 6 degrees of freedom the law of equipartition of energy gives the following relation between the molecular specific heat $\left( {{C_V}} \right)$ and gas constant $\left( R \right)$

Which of the following is incorrect regarding the assumptions of kinetic theory of gases?

According to the kinetic theory of gases the $r.m.s$ velocity of gas molecules is directly proportional to

According to the kinetic theory of gases, the pressure exerted by a gas on the walls is measured as

The ratio of mean kinetic energy of hydrogen and oxygen at a given temperature is

Assertion (A) : In equation $p=\frac{1}{3} \alpha v_{\text {rms }}^2$, the term $\alpha$ represents density of gas.

Reason (R) : $v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}$.

Assertion (A) Assertion The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and volume.

Reason (R) The molecules of gas collide with each other and the velocities of the molecules change due to the collision.

The root mean square speed of the molecules of a gas is

Assertion: The ratio $C_p / C_v$ is more for helium gas than for hydrogen gas.
Reason: All metals acts as black bodies.

If Maxwell distribution is valid and $v_p$ denotes the most probable speed, $v_{av}$ is the average speed and $v_{rms}$ is the root-mean-square speed, then

Relation between the ratio of specific heats $\left( \gamma \right)$ of gas and degree of freedom 'f' will be

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :

The specific heat of an ideal gas is

The average translational kinetic energy of ${O}_2$ (molar mass 32) at a particular temperature is $0.048 \mathrm{~eV}$. The average translational kinetic energy of ${N}_2$ (molar mass 28) molecules (in $\mathrm{eV}$) at the same temperature is

Find the ratio of specific heat at constant pressure to the specific heat constant volume for $N{H_3}$

Assertion: Vibrational degree of freedom of a di-atomic gas molecule appears at very high temperature
Reason: Di-atomic gas has two vibrational degree of freedom in one direction.

The R.M.S. speed of oxygen molecules at temperature ${T}$ (in kelvin) is ${v} \,{ms}^{-1}$. As the temperature becomes $4 {~T}$ and the oxygen gas dissociated into atomic oxygen, then the speed of atomic oxygen