Kinetic Theory PYQs

A flask contains argon and chlorine in the ratio of $2:1$ by mass. The temperature of the mixture is $27^\circ C$. The ratio of root mean square speed of the molecules of the two gases $\left(\dfrac{v_{\mathrm{rms}}^{\mathrm{Ar}}}{v_{\mathrm{rms}}^{\mathrm{Cl}}}\right)$ is: (Atomic mass of argon $=40.0\,u$ and molecular mass of chlorine $=70.0\,u$)

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27°C. The mass of oxygen withdrawn from the cylinder is nearly equal to : [Given, R = 100/12 J mol⁻¹ K⁻¹ and molecular mass of O₂ = 32, 1 atm pressure = 1.01 × 10⁵ N/m]

Which amongst the following options is correct graphical representation of Boyle’s Law?

The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is:

Match Column-I and Column-II and choose the correct match from the given choices.

A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27°C. Its density is : (R = 8.3 J mol⁻¹ K⁻¹)

The mean free path for a gas, with molecular diameter $d$ and number density $n$ can be expressed as:

The average thermal energy for a mono-atomic gas is : (k$_B$ is Boltzmann constant and T, absolute temperature)

The value of $\gamma\left(=\frac{C_p}{C_v}\right)$ for hydrogen, helium and another ideal diatomic gas X (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to,

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given: Mass of oxygen molecule $m = 2.76 \times 10^{-26}$ kg, Boltzmann constant $k_B = 1.38 \times 10^{-23}$ JK$^{-1}$)

A gas mixture consists of $2$ moles of $O_2$ and $4$ moles of Ar at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is:

A given sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T$. The mass of each molecule of the gas is $m$. Which of the following gives the density of the gas?

Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is:

The mean free path of molecules of a gas, (radius 'r') is inversely proportional to:

The amount of heat energy required to raise the temperature of $1\,g$ of Helium at NTP, from $T_1\,K$ to $T_2\,K$ is

If $c_p$ and $c_v$ denote the specific heats (per unit mass) of an ideal gas of molecular weight M where R is the molecular weight constant, then

At 10°C the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At 110°C this ratio is

If a gas expands at constant temperature, it indicates that

The molar specific heat at constant pressure of an ideal gas is (7/2)R. The ratio of specific heat at constant pressure to that at constant volume is: