# Class 11 Physics Chapter 13 Important Questions Kinetic Theory

It is important for the students that all the concepts should be very clear for better marks in future. Here, we are providing important conceptual questions and answers for class 11 physics chapter 13 Kinetic Theory. In this lesson, students will learn about Kinetic Theory. This will not only help the students to know the important questions but will also help them during revision.

Q. 1. How is pressure of an ideal gas related to number of molecules per unit volume of gas?
Ans. As per ideal gas equation, pressure P of a gas is directly proportional to n, the number of gas molecules per unit volume. Thus, P ∝ n. In fact, P = nkBT, where T is the temperature of the gas.

Q. 2. Name two phenomena which provide direct experimental evidence in support of molecular motion in a gas.
Ans. The phenomena of diffusion of gases and Brownian motion (random motion of pollen grain particles in a solution) provide direct experimental evidence in support of molecular motion in a gas.

Q. 3. How does the small of a burning incense stick (an agarbatti) spread throughout the room even in still air?
Ans. The smell of a burning incense stick spreads throughout the room even in still air on account of random, incessant motion of perfume molecules throughout the room.

Q. 4. What justification is there in neglecting the effect of change in gravitational potential energy of molecules while dealing with kinetic theory of gases?
Ans. Magnitude of change in gravitationl potential energy is extremely small as compared to average value of kinetic energy of gas molecules. Hence, we are justified in neglecting the effect of change in gravitational potential energy of molecules.

Q. 5. For which gas at STP condition is the rms speed of gas molecules maximum, and why?
Ans. The rms speed of hydrogen gas moleclues is maximum at STP condition (or at any temperature and pressure condition) as compared to all other gases because molar mass of hydrogen gas (or the density) is minimum and

v_{rms}\prop\frac{1}{\sqrt{M_0}}

Q. 6. The number of molecules of a gas (or the mass of gas enclosed) in a container is doubled. What will be the effect on the rms speed of gas molecules?
Ans. The rms speed of gas molecules remains unchanged because it does not depend on number of molecules present (or mass of gas).

Q. 7. Helium, nitrogen and carbon dioxide gases are maintained at 15°C temperature. Which gas has maximum average value of translational kinetic energy of a molecule, and why?
Ans. Molecules of all the three gases will have same average kinetic energy of translation having a value \frac{3}{2}K_{B}T, where T = 288 K.

Q. 8. How does the mean free path of molecules of a gas depend on its (a) temperature (b) pressure
Ans. The value of mean free path of molecules of a gas is:

(a) proportional to its absolute temperature, and

(b) inversely proportional to its pressure.

Q. 9. Neglecting the vibrational modes, write the number of degrees of freedom per molecule of a

• (a) monoatomic
• (b) diatomic
• (c) polyatomic gas

Ans. If vibrational modes are neglected, then number of degrees of freedom per molecule in a

(a) monoatomic gas is 3

(b) diatomic gas is 5

(c) polyatomic gas is 6

Q. 10. A cylinder fitted with a piston contains one mole of oxygen and two moles of nitrogen at room temperature. Find the ratio of average internal energy per molecule of these gases.
Ans. As both the gases are diatomic gases and have equal numbers of degrees of freedom. Hence, average value of their internal energy per molecule will be exactly same or the ratio will be 1.

Q. 11. Under what condition does a real gas behave almost like an ideal gas and why?
Ans. A real gas approximately behaves like an ideal gas under the conditions of high temperature and low pressure. Because at these conditions, volume of the gas is high and intermolecular distance is comparatively larger. Consequently, intermolecular interactions are negligible and gas may be considered as an ideal gas.

Q. 12. When volume of a given mass of a gas is reduced at constant temperature, the gas pressure increases. How will you explain this fact on the basis of kinetic theory of gases?
Ans. When at constant temperature, volume of a given mass of a gas is reduced then number of molecules per unit volume increases. Due to increase in molecular density, the gast pressure increases because as per kinetic theory P=\frac{1}{3}nm\bar{v}^2, where n is the number of molecules per unit volume.

Q. 13. A certain mass of gas is enclosed in a container. When temperature of the gas is raised, its pressure rises. How will you explain this on the basis of kinetic theory of gases?
Ans. As per kinetic interpretation of temperature, the average kinetic energy of gas molecules is proportional to its absolute temperature. When temperature of a gas is raised, the value of kinetic energy and hence rms speed of gas molecules increases. As a result, during each collision a molecule will impart greater momentum to a wall of container. Moreover, due to increase in rms speed, frequency of collision of molecules with a wall increases. Thus, a greater momentum is transferred per unit time to the wall and consequently, gas pressure increases.

Q. 14. Does a gas exert pressure only on the walls of container or throughout the gas?
Ans. Pressure of a gas is not exerted on the walls of container only. Pressure exists everywhere in a gas. Any layer of gas inside the volume of a container is in equilibrium because the pressure is the same on both sides of the layer.

Q. 15. Under STP condition, which will have greater number of molecules one litre of hydrogen or one litre of oxygen? It is given that for a given volume at STP, mass of oxygen gas is 16 times that of hydrogen.
Ans. As per Avogadro's law, under identical conditions of temperature and pressure, equal volumes of all gases contain equal number of molecules. Hence, number of molecules in 1 litre of oxygen at STP condition will be exactly same as that for hydrogen. The number of molecules is independent of the molecular mass of the gas.

Q. 16. Why does the temperature of a gas rise when the gas is suddenly compressed? Explain on the basis of kinetic theory of gases.
Ans. When a gas is suddenly compressed, the volume of the gas is reduced and so the number of gas molecules per unit volume increases. As a result, the kinetic energy of gas molecules per unit volume increases. Consequently, temperature of the gas rises.

Q. 17. Show that as per kinetic theory of gases a temperature less than 0 K is not possible.
Ans. As per kinetic theory of gases, the average translational kinetic energy of a molecule is proportional to its absolute temperature. At absolute zero (0 K) temperature, the kinetic energy of any molecule of gas is zero. If we consider a temperature even less than 0 K, then kinetic energy of gas molecules should further fall, i.e., it should become negative which is impossible. As a result, it is clear that a temperature less than 0 K is not possible.

Q. 18. The average translational kinetic energy of oxygen molecules (relative molar mass = 32) at a particular temperature is 0.48 eV. What will be the translational kinetic energy of nitrogen molecules (relative molar mass = 28) in eV at the same temperature?
Ans. We know that the average translational 3 kinetic energy of a gas molecule is \frac{3}{2}K_{B}T and is independent of the mass of gas molecules. Hence, at a given temperature, average translational kinetic energy of a nitrogen molecule = average translational kinetic energy of an oxygen molecule 0.48 eV.

Q. 19. What is the significance of Brownian motion in kinetic theory of gases?
Ans. Brownian motion is the exprimentally observed zig-zag motion of pollen grains (microscopic particles) suspended in water when viewed under a microscope. This motion provides a much needed experimental evidence for incessant motion of molecules of a gas. Brownian motion also provided a technqiue to correlate the mean free path with size of a microscopic particle.

Q. 20. Are you talking in terms of rms speed or rms velocity of gas molecules while discussing kinetic theory of gases? Why?
Ans. We usually talk in terms of rms speed of gas molecules because by its basic definition, we are considering only the magnitudes of molecular velocities and are ignoring their directions.

Q. 21. Although speed of individual air molecules is of the order of 0.5 km/s at room temperature, yet the smell of a scent spreads at a much slower rate. Why?
Ans. Of course, speed of individual air molecules is of the order of 0.5 km s but the molecules are in a state of incessant motion and frequently collide among themselves. In each collision, the speed and direction of motion of a molecule changes. Thus, net distance covered by scent or perfume molecules per unit time is extremely small and only of the order of few millimetres per second. It is due to this reason that smell of scent takes a long time (few minutes) to spread in a room.

Q. 22. Why do molecules of air in a room not fall and settle on the ground under the action of gravity?
Ans. Molecules of air in a room do not fall and settle on the ground because of their high speeds and incessant collisions. In equilibrium state, there is a very slight increase in density at lower heights. The effect is extremely small because the gravitational potential energy mgh of molecule for ordinary height is much less than the average kinetic energy \frac{1}{2}mv_{rms}^2` of molecule.

Q. 23. Explain why there is practically no atmosphere on the surface of the Moon.
Ans. We know that molecules of a gas are in a state of incessant motion and molecular speeds vary over a large range. Escape speed at the surface of moon is even less than 2.4 km/s. So, those molecules of the Moon atmosphere gradually escaped from moon's surface whose molecular speed was more than 2.4 km/s. Due to molecular collisions, more molecules acquired speeds greater than 2.4 km/s and gradually escaped. Over a long time, spanning over millions of years, gas molecules continued escaping from the moon's atmosphere. Consequently, at present practically there is no atmosphere left on the surface of the moon.

Q. 24. Lighter gases like hydrogen and helium are the Earth's atmosphere. Explain why.
Ans. We know that gas molecules are in a state of incessant motion and speeds of molecules of lighter gases like hydrogen and helium is much greater than that for heavier gases like N₂, O₂, etc. Those molecules of hydrogen and helium slowly and steadily escaped from the Earth's atmosphere whose speeds were greater than the value of escape speed for the Earth (about 11.2 km/s). Of course, the process should be an extremely slow process but over a period of billions of years since the formation of the earth the process continues. As a result, at present hydrogen and helium gases are practically absent in the Earth's atmosphere.

Q. 25. Can you suggest a kinetic interpretation of evaporation process?
Ans. Evaporation is a slow process which takes place from the free surface of a liquid at all temperatures. As per kinetic theory at a given temperature, even in a liquid, molecules are under going random motion with varying speeds. High speed molecules of a liquid due to their high value of kinetic energy may overcome the intermolecular attractive force due to neighbouring liquid molecules and hence may vaporise and escape from the surface of liquid, thus, giving rise to the phenomenon of evaporation.