Kinetic Theory

The molecules of a given mass of a gas have r.m.s. velocity of 200 ms⁻¹ at 27 °C and 1.0 × 10⁵ Nm⁻² pressure. When the temperature and pressure of the gas are respectively 127 °C and 0.05 × 10⁵ Nm⁻², the r.m.s. velocity of its molecules in ms⁻¹ 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?

A gas mixture consists of 2 moles of O₂ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given: mass of an oxygen molecule m = 2.76 × 10⁻²⁶ kg, Boltzmann constant k_B = 1.38 × 10⁻²³ J K⁻¹, escape speed = 11200 ms⁻¹)

An ideal gas expands isothermally from 10⁻³ m³ to 10⁻² m³ at 300 K against a constant external pressure of 10⁵ N m⁻². The work done on the gas is:

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

The average thermal energy for a mono-atomic gas is: (k_B is the Boltzmann constant and T the absolute temperature)

Match Column-I with Column-II and choose the correct match from the given choices: Column-I (A) Root mean square speed of gas molecules (B) Pressure exerted by ideal gas (C) Average kinetic energy of a molecule (D) Total internal energy of 1 mole of a diatomic gas Column-II (i) ⅓ n m v²_rms (ii) √(3RT/M) (iii) (5/2) RT (iv) (3/2) k_B T Choose the correct match:

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

A container of volume 200 cm³ contains 0.2 mole of hydrogen gas and 0.3 mole of argon gas. The pressure of the system at temperature 200 K (R = 8.3 J K⁻¹ mol⁻¹) will be:

The temperature of a gas is −50 °C. To what temperature should the gas be heated so that the rms speed is increased by 3 times?

The values of Cp/Cv for hydrogen, helium and another ideal diatomic gas X (whose molecules are not rigid but have an additional vibrational mode) are respectively equal to:

The volume occupied by 1.8 g of water vapour at 374 °C and 1 bar pressure will be: [Use R = 0.083 bar L K⁻¹ mol⁻¹]

The following graph represents the T–V curves of an ideal gas (where T is the temperature and V the volume) at three pressures P₁, P₂ and P₃, compared with those of Charles's law represented as dotted lines. Then the correct relation is:

A container has two chambers of volumes V₁ = 2 litres and V₂ = 3 litres separated by a partition made of a thermal insulator. The chambers contain n₁ = 5 and n₂ = 4 moles of ideal gas at pressures p₁ = 1 atm and p₂ = 2 atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of:

Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius r_A and r_B, respectively. On supplying an equal amount of heat to both systems reversibly under constant pressure, the pistons of gas A and gas B are displaced by 16 cm and 9 cm, respectively. If the change in their internal energy is the same, then the ratio r_A/r_B is equal to:

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its pressure drops to 11 atmospheric pressure at temperature 27 °C. The mass of the oxygen withdrawn from the cylinder is nearly equal to: [Given R = 100/12 J mol⁻¹ K⁻¹, molecular mass of O₂ = 32, 1 atm = 1.01 × 10⁵ N m⁻²]

The mean free path of molecules in an ideal gas $A$ is half that of another ideal gas $B$. The diameter of the spherical molecules of gas $A$ is twice the diameter of the molecules of $B$. If the number densities of gases $A$ and $B$ are $n_A$ and $n_B$ respectively, the correct option is:

An ideal gas is made of polyatomic molecules. Each molecule has three translational, three rotational and $f$ vibrational modes. If the ratio of heat capacities $C_P/C_V$ of the gas is $8/7$, then the value of $f$ is:

A flask contains argon and chlorine in the ratio of 2 : 1 by mass. The temperature of the mixture is 27 °C. The ratio of root mean square speeds of the molecules of the two gases (v_rms^Ar / v_rms^Cl) is: (Atomic mass of argon = 40.0 u and molecular mass of chlorine = 70.0 u)