HC Verma Questions and Solutions: Chapter 24: Kinetic Theory of Gases- 1 | HC Verma Solutions - JEE PDF Download

Q.1. When we place a gas cylinder on a van and the van moves, does the kinetic energy of the molecules increase? Does the temperature increase?

No, kinetic energy of the molecules does not increase. This is because velocity of the molecules does not increase with respect to the walls of the gas cylinder, when the cylinder is kept in a vehicle moving with a uniform motion. However, if the vehicle is accelerated or decelerated, then there will be a change in the gas's kinetic energy and there will be a rise in the temperature. 

Q.2. While gas from a cooking gas cylinder is used, the pressure does not fall appreciably till the last few minutes. Why?

Inside a cooking gas cylinder, the gas is kept in the liquid state using high pressure. Boiling point of a liquid depends on the pressure above its surface. Higher the pressure above the liquid, higher will be its boiling point.
When the gas oven is switched on, the vapour pressure inside the cylinder decreases. To compensate this fall in pressure, more liquid undergoes phase transition (vapourisation) to build up the earlier pressure. In this way, more and more gas evaporates from the liquified state at constant pressure.    

Q.3. Do you expect the gas in a cooking gas cylinder to obey the ideal gas equation?

No, the gas won't obey ideal gas equation due to the following reasons:
1. In a cooking gas cylinder, the gas is kept at high pressure and at room temperature. Real gases behave ideally only at low pressure and high temperature.
2. Cooking gas is kept in liquid state inside the cylinder becaue liquid state does not obey the ideal gas equation. 

Q.4. Can we define the temperature of (a) vacuum, (b) a single molecule?

(a) Temperature is defined as the average kinetic energy of he partciles. In a vacuum, devoid of any electromagnetic fields and molecules or entities, the temperature cannot be defined as there are no molecules or atoms or entities.
(b) No, we cannot define temperature of a single molecule. Since temperature is defined as the average kinetic energy of the particles, it is defined only statistically for a large collection of molecules. 

Q.5. Comment on the following statement: the temperature of all the molecules in a sample of a gas is the same.

Yes, at equilibrium all the molecules in a sample of gas have the same temperature. This is because temperature is defined as the average kinetic energy for all the molecules in a system. Since all the molecules have the same average, temperature will be the same for all the molecules.

Q.6. Consider a gas of neutrons. Do you expect it to behave much better as an ideal gas as compared to hydrogen gas at the same pressure and temperature?

Yes, according to the postulates of kinetic theory, a gas of neutrons will be a better ideal gas than hydrogen. The reasons are given below:
1. As per the Kinetic theory, neutrons do not interact with each othe. Molecules of an ideal gas should also not interact with each other. On the other hand, hydrogen molecules interact with each other owing to the presence of charges in them.
2. Neutrons are smaller than hydrogen. This fulfils another kinetic theory postulate that gas molecules should be points and should have negligible size. 

Q.7. A gas is kept in a rigid cubical container. If a load of 10 kg is put on the top of the container, does the pressure increase?

No, the pressure on gas won't increase because of this. The pressure will not be transferred to the gas, but to the container and to the ground.  

Q.8.  If it were possible for a gas in a container to reach the temperature 0 K, its pressure would be zero. Would the molecules not collide with the walls? Would they not transfer momentum to the walls?

Since the pressure would be zero, the molecules would not collide with the walls and would not transfer momentum to the walls. This is because pressure of a gas is formed due to the molecule's collision with the walls of the container.  

Q.9. It is said that the assumptions of kinetic theory are good for gases having low densities. Suppose a container is so evacuated that only one molecule is left in it. Which of the assumptions of kinetic theory will not be valid for such a situation? Can we assign a temperature to this gas?

Two postulates of kinetic theory will not be valid in this case. These are given below:
1. All gases are made up of molecules moving randomly in all directions
2. When a gas is left for a sufficient time, it comes to a steady state. The density and the distribution of molecules with different velocities are independent of position, direction and time. 

Q.10. A gas is kept in an enclosure. The pressure of the gas is reduced by pumping out some gas. Will the temperature of the gas decrease by Charles's low?

If the gas is ideal, there will be no temperature change. Moreover, Charles's law relates volume with temperature not pressure with temperature, so the cause behind the phenomena cannot be explained by Charles's law.

Q.11. Explain why cooking is faster in a pressure cooker.

In a pressure cooker, the vapour pressure over the water surface is more than the atmospheric pressure. This means boiling point of the water will be higher in the pressure cooker than in the open. This will let the cereals and food to be cooked in higher temperature than at 100°C,. Thus, cooking process gets faster.

Q.12. If the molecules were not allowed to collide among themselves, would you expect more evaporation or less evaporation?

If the molecules are not allowed to collide with each other, they will have long mean free paths and hence, evaporation will be faster. In vacuum, the external pressure will be very low. So, the liquid will boil and evaporate at very low temperature.  

Q.13. Is it possible to boil water at room temperature, say 30°C? If we touch a flask containing water boiling at this temperature, will it be hot?

 Yes, it is possible to boil water at 30°C by reducing the external pressure. A liquid boils when its vapour pressure equals external pressure. By lowering the external pressure, it is possible to boil the liquid at low temperatures.

No, the flask containing water boiling at 30°C will not be hot.

Q.14. When you come out of a river after a dip, you feel cold. Explain.

After a dip in the river, the water that sticks to our body gets evaporated. We know that evaporation takes place faster for higher temperatures. Thus, the molecules that have the highest kinetic energy leave faster and that is how heat is given away from our body.

As a result of it, temperature of our body falls down due to loss of heat and we feel cold.

Question for HC Verma Questions and Solutions: Chapter 24: Kinetic Theory of Gases- 1

Try yourself:Figure shows graphs of pressure vs density for an ideal gas at two temperatures T₁ and T₂.

• A.

  T₁ > T₂
• B.

  T₁ = T₂
• C.

  T₁ < T₂
• D.

  Any of the three is possible.

Explanation

The straight line T1 has greater slope than T​2. This means  ratio is greater for T1 than T2. Now, rms velocity of a gas is given by   This means rms velocity of gas with T1 molecules is greater than T2 molecules. Again, gas with higher temperature has higher rms velocity.
So, T1 > T2.

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Question for HC Verma Questions and Solutions: Chapter 24: Kinetic Theory of Gases- 1

Try yourself:The process on an ideal gas, shown in figure, is

• A.

  isothermal
• B.

  isobaric
• C.

  isochoric
• D.

  none of these

Explanation

According to the graph, P is directly proportional to T.
Applying the equation of state, we get
PV = nRT

This means nR/V is  a  constant . So, V is also a constant.
Constant V implies the process is isochoric.

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Question for HC Verma Questions and Solutions: Chapter 24: Kinetic Theory of Gases- 1

Try yourself:Consider the quantity  of an ideal gas where M is the mass of the gas. It depends on the

• A.

  temperature of the gas
• B.

  volume of the gas
• C.

  pressure of the gas
• D.

  nature of the gas.

Explanation

In an ideal gas, the equation of state is given by 

Multiplying both sides by mass of the gas M, we get 
Now, n N_A gives the total number of molecules of the gas. Also  gives the mass of a single molecule. Hence,  is the mass of a single molecule of the gas, Molecular mass is a property of the gas.

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