Kinetic theory of gases practice · Mixed difficulty

At $0^\circ \,K$ which of the following properties of a gas will be zero?

When an ideal gas is compressed adiabatically, its temperature rises the molecules on the average have more kinetic energy than before. The kinetic energy increases

One mole of an ideal diatomic gas undergoes a process $P=\frac{P_0}{\left(1+\frac{V}{V_0}\right)^3}$, where $P_0$ and $V_0$ are positive constants. The translational kinetic energy of the gas when $V=V_0$ is given by

If an ideal flask containing hot coffee is shaken, the temperature of the coffee will

The ratio of the molar heat capacities of a diatomic gas at constant pressure to that at constant volume is

The ratio of rms speed of an ideal gas molecules at pressure $p$ to that at pressure $2 p$ is

If mass of $He$ atom is 4 times that of hydrogen atom then mean velocity of $He$ is

Some gas at 300 K is enclosed in a container. Now, the container is placed on a fast moving train. While the train is in motion, the temperature of the gas

If ${V_H},{V_N}$ and ${V_0}$ denote the root –mean square velocities of molecules of hydrogen, nitrogen and oxygen respectively at a given temperature, then

In van der Waals’ equation, the critical pressure $\mathrm{P_c}$ is given by

The ratio of the molecular masses of two gases is 7/8. What is the ratio of the number of moles of two gases, if they are in two different containers and have same mass for each gas?

The rms speed of a large number of molecules of a gas in a vessel is $600 \mathrm{~m} \mathrm{~s}^{-1}$. If $25 \%$ of the gas leaks out at constant temperature, then rms speed of the remaining molecules will be

Let $A$ and $B$ the two gases and given $\frac{{{T_B}}}{{{M_A}}} = 4.\frac{{{T_B}}}{{{M_B}}};$ where $T$ is the temperature and $M$ is molecular mass. If ${C_A}$ and ${C_B}$ are the $r.m.s.$ speed, then the ratio $\frac{{{C_A}}}{{{C_B}}}$ will be equal to

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

The temperature of gas is produced by

Vapour is injected at a uniform rate in a closed vessel which was initially evacuated. The pressure in the vessel

Given below are two statements:

Statement (I): The mean free path of gas molecules is inversely proportional to square of molecular diameter.

Statement (II): Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.

In the light of the above statements, choose the correct answer from the option given below:

For a gas at a temperature $T$ the root-mean-square velocity ${v_{rms}},$ the most probable speed ${v_{mp}},$ and the average speed ${v_{av}}$ obey the relationship

If $\gamma$ be the ratio of specific heats of a perfect gas, the number of degrees of freedom of a molecule of the gas is

The average kinetic energy of a gas molecules is

A gas cylinder of 50 litres capacity contained helium at 80 atmospheric pressure. Due to slow leakage it was found after a while that the pressure had dropped to 40 atmosphere. Find the proportion of the gas that has escaped and also the volume the escaped gas would occupy at atmospheric pressure.

Root mean square velocity of a particle is $v$ at pressure $P.$ If pressure is increased two times, then the $r.m.s.$ velocity becomes

Imagine a planet whose diameter and mass are both one half of those of Earth. The day's temperature of this planet's surface reaches up to $800 \mathrm{~K}$. Find whether oxygen molecules are possible in the atmosphere of this planet.

Kinetic theory of gases provide a base for

Mean free path of ${O}_2$ gas molecules in rigid container is $\lambda$. The temperature of gas is doubled, then new mean free path of ${O}_2$ gas molecules is

Let $A$ and $B$ the two gases and given $\frac{{{T_B}}}{{{M_A}}} = 4.\frac{{{T_B}}}{{{M_B}}};$ where $T$ is the temperature and $M$ is molecular mass. If ${C_A}$ and ${C_B}$ are the $r.m.s.$ speed, then the ratio $\frac{{{C_A}}}{{{C_B}}}$ will be equal to

The temperature of argon, kept in a vessel, is raised by ${1^ \circ }C$ at a constant volume. The total heat supplied to the gas is a combination of translation and rotational energies. Their respective shares are

Let $\mathrm{V}$ denote the root mean square speed of the molecules in an ideal diatomic gas at absolute temperature $\mathrm{T}$. The mass of a molecule is ' $m$ '. Neglecting vibrational energy terms, which is false?

Two identical containers $\mathrm{A}$ and $\mathrm{B}$ have frictionless pistons. They contain the same volume of a ideal gas at the same temperature. The mass of the gas in $\mathrm{A}$ is $\mathrm{m}_{\mathrm{A}}$ and that in $\mathrm{B}$ is $\mathrm{mB}$. The gas in each cylinder is now allowed to expand isothermally to double the initial volume. The changes in the pressure in A and B are found to be $\Delta p$ and $1.5 \Delta p$ respectively.

The equation of state of a gas is given by $\left( {P + \frac{{a{T^2}}}{V}} \right){V^c} = \left( {RT + b} \right),$ where $a,b,c$ and $R$ are constants. The isotherms can be represented by $P = A{V^m} - B{V^n},$ where $A$ and $B$ depend only on temperature and