NCERT Exemplar solutions for Physics [English] Class 11 chapter 13 - Kinetic Theory [Latest edition]

A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500 ms^–1 in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground ______.

1 mole of an ideal gas is contained in a cubical volume V, ABCDEFGH at 300 K (Figure). One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At any given time ______.

Boyle’s law is applicable for an ______.

A cylinder containing an ideal gas is in vertical position and has a piston of mass M that is able to move up or down without friction (Figure). If the temperature is increased ______.

Volume versus temperature graphs for a given mass of an ideal gas are shown in figure at two different values of constant pressure. What can be inferred about relation between P₁ and P₂?

1 mole of H₂ gas is contained in a box of volume V = 1.00 m³ at T = 300K. The gas is heated to a temperature of T = 3000K and the gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal) ______.

A vessel of volume V contains a mixture of 1 mole of Hydrogen and 1 mole of Oxygen (both considered as ideal). Let f₁(v)dv, denote the fraction of molecules with speed between v and (v + dv) with f₂(v)dv, similarly for oxygen. Then ______.

An inflated rubber balloon contains one mole of an ideal gas, has a pressure p, volume V and temperature T. If the temperature rises to 1.1 T, and the volume is increased to 1.05 V, the final pressure will be ______.

ABCDEFGH is a hollow cube made of an insulator (Figure). Face ABCD has positive charge on it. Inside the cube, we have ionized hydrogen. The usual kinetic theory expression for pressure ______.

1. will be valid.
2. will not be valid since the ions would experience forces other than due to collisions with the walls.
3. will not be valid since collisions with walls would not be elastic.
4. will not be valid because isotropy is lost.

Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory `pV = 2/3` E, E is ______.

1. the total energy per unit volume.
2. only the translational part of energy because rotational energy is very small compared to the translational energy.
3. only the translational part of the energy because during collisions with the wall pressure relates to change in linear momentum.
4. the translational part of the energy because rotational energies of molecules can be of either sign and its average over all the molecules is zero.

In a diatomic molecule, the rotational energy at a given temperature ______.

1. obeys Maxwell’s distribution.
2. have the same value for all molecules.
3. equals the translational kinetic energy for each molecule.
4. is (2/3)rd the translational kinetic energy for each molecule.

Which of the following diagrams (Figure) depicts ideal gas behaviour?

(a)	(b)
(c)	(d)

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 ______.

1. because of collisions with moving parts of the wall only.
2. because of collisions with the entire wall.
3. because the molecules gets accelerated in their motion inside the volume.
4. because of redistribution of energy amongst the molecules.

Calculate the number of atoms in 39.4 g gold. Molar mass of gold is 197g mole^–1.

The volume of a given mass of a gas at 27°C, 1 atm is 100 cc. What will be its volume at 327°C?

The molecules of a given mass of a gas have root mean square speeds of 100 ms⁻¹ at 27°C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127°C and 2.0 atmospheric pressure?

Two molecules of a gas have speeds of 9 × 10 6 ms⁻¹ and 1 × 106 ms⁻¹, respectively. What is the root mean square speed of these molecules?

A gas mixture consists of 2.0 moles of oxygen and 4.0 moles of neon at temperature T. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.)

Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1 A and 2 A. The gases may be considered under identical conditions of temperature, pressure and volume.

The container shown in figure has two chambers, separated by a partition, of volumes V₁ = 2.0 litre and V₂ = 3.0 litre. The chambers contain µ₁ = 4.0 and µ₂ = 5.0 moles of a gas at pressures p₁ = 1.00 atm and p₂ = 2.00 atm. Calculate the pressure after the partition is removed and the mixture attains equilibrium.

A gas mixture consists of molecules of types A, B and C with masses m_A > m_B > m_C. Rank the three types of molecules in decreasing order of average K.E.

A gas mixture consists of molecules of types A, B and C with masses m_A > m_B > m_C. Rank the three types of molecules in decreasing order of rms speeds.

We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm kept at NTP. The gas in the chamber is compressed keeping the temperature constant till a final pressure of 100 atm. Is one justified in assuming the ideal gas law, in the final state?

(Hydrogen molecules can be consider as spheres of radius 1 Å).

When air is pumped into a cycle tyre the volume and pressure of the air in the tyre both are increased. What about Boyle’s law in this case?

A ballon has 5.0 g mole of helium at 7°C. Calculate

1. the number of atoms of helium in the balloon
2. the total internal energy of the system.

Calculate the number of degrees of freedom of molecules of hydrogen in 1 cc of hydrogen gas at NTP.

An insulated container containing monoatomic gas of molar mass m is moving with a velocity v_o. If the container is suddenly stopped, find the change in temperature.

Explain why there is no atmosphere on moon.

Explain why there is fall in temperature with altitude.

Consider an ideal gas with following distribution of speeds.

Calculate V_rms and hence T. (m = 3.0 × 10⁻²⁶ kg)

Consider an ideal gas with following distribution of speeds.

If all the molecules with speed 1000 m/s escape from the system, calculate new V_rms and hence T.

Ten small planes are flying at a speed of 150 km/h in total darkness in an air space that is 20 × 20 × 1.5 km³ in volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are. On the average about how long a time will elapse between near collision with your plane. Assume for this rough computation that a saftey region around the plane can be approximated by a sphere of radius 10 m.

A box of 1.00 m³ is filled with nitrogen at 1.50 atm at 300K. The box has a hole of an area 0.010 mm². How much time is required for the pressure to reduce by 0.10 atm, if the pressure outside is 1 atm.

Consider a rectangular block of wood moving with a velocity v₀ in a gas at temperature T and mass density ρ. Assume the velocity is along x-axis and the area of cross-section of the block perpendicular to v₀ is A. Show that the drag force on the block is `4ρAv_0 sqrt((KT)/m)`, where m is the mass of the gas molecule.