Kinetic theory of gases practice · Mixed difficulty

In the expression for $V_{r m s}$ of a mixture of 2 gases at same temperature, $V_{r m s}=\sqrt{\frac{3 R T}{M}}$, the molecular weight $\mathrm{M}$ is

With increase in pressure at constant temperature, rms speed of gases

Pressure of a gas at constant volume is proportional to

For a real gas (van der Waal’s gas)

Calculate the ratio of rms speeds of oxygen gas molecules to that of hydrogen gas molecules kept at the same temperature.

The average kinetic energy per mole of hydrogen at given temperature is

The number of translational degrees of freedom for a diatomic gas is

If the earth did not have atmosphere, the temperature would be

Assertion: A gas is kept in an insulated cylinder with a movable piston, in compressed state. As the piston is released, temperature of the gas decreases.
Reason: According to the kinetic theory of gas, a molecule colliding with the piston must rebound with less speed than it had before the collision. Hence average speed of the molecules is reduced.

The temperature of a gas is held constant, while its volume is decreased. The pressure exerted by its volume is decreased. The pressure exerted by the gas on the walls of the container increases, because its molecules

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

The critical volume of a gas obeying van der Waals' equation is

For a gas at $300 \mathrm{~K}$ temperature energy is $300 \mathrm{~J}$ and speed is $300 \mathrm{~m} /$ sec. If temperature is made 2 times of initial then find out the final energy and speed.

The value of molar specific heat at constant volume for 1 mole of polyatomic gas having $n$ number of degrees of freedom at temperature $T \, K$ is (here, $R=$ universal gas constant)

Molecules of a gas behave like

Two gases occupy two containers $\mathrm{A}$ and $\mathrm{B}$ the gas in $\mathrm{A}$, of volume $0.10 \mathrm{~m}^3$, exerts a pressure of $1.40 \mathrm{MPa}$ and that in $\mathrm{B}$ of volume $0.15 \mathrm{~m}^3$ exerts a pressure $0.7 \mathrm{MPa}$. The two containers are united by a tube of negligible volume and the gases are allowed to intermingle. Then if the temperature remains constant, the final pressure in the container will be (in $\mathrm{MPa}$ )

Assertion : Vibrational energy of particle at temperature T is kT.

Reason : For every particle, vibrational degree of freedom is 2.

Increase in temperature of a gas filled in a container would lead to:

If three molecules of oxygen at $27^{\circ} \mathrm{C}$ have velocities $0.5 \mathrm{~km} / \mathrm{s}, 1 \mathrm{~km} / \mathrm{s}$ and $2 \mathrm{~km} / \mathrm{s}$ respectively. Then their root mean square speed will be

Speed of sound in a gas is $v$ and $r.m.s.$ velocity of the gas molecules is $c.$ The ratio of $v$ to $c$ is

For Boyle’s law to hold good, the gas should be

A cylinder rolls without slipping down an inclined plane, the number of degrees of freedom it has, is

What is the average velocity of the molecules of an ideal gas?

The velocity of 4 gas molecules are given by 1 km/s, 3 km/s, 5 km/s and 7 km/s. Calculate the difference between average and rms velocity.

According to the kinetic theory of gases, at absolute temperature

At identical temperatures, the rms speed of hydrogen molecules is 4 times that for oxygen molecules. In a mixture of these in mass ratio $\mathrm{H}_2: \mathrm{O}_2=1: 8$, the rms speed of all molecules is $\mathrm{n}$ times the rms speed for $\mathrm{O}_2$ molecules, where $\mathrm{n}$ is

The internal energy $\left( U \right)$, pressure $\left( p \right)$ and volume $\left( V \right)$ of an ideal gas are related as $U = 3pV + 4$. The gas is

A polyatomic gas with n degrees of freedom has a mean energy per molecule given by
($N$ is Avogadro’s number)

A flask contains Hydrogen and Argon in the ratio $2: 1$ by mass. The temperature of the mixture is $30^{\circ} \mathrm{C}$. The ratio of average kinetic energy per molecule of the two gases ( $\mathrm{K}$ argon/ $\mathrm{K}$ hydrogen) is:
(Given : Atomic Weight of $\mathrm{Ar}=39.9$ )

Statement-I: Boltzmann's constant is a gas constant for 1 molecule of a gas
Statement-II: Universal gas constant is a gas constant for 1 mole of a gas