NCERT Class 11 Physics Chapter 13 Kinetic Theory CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 27:

Explain why

(a) There is no atmosphere on moon.

(b) There is fall in temperature with altitude.

Answer:

The moon has small gravitational force and hence the escape velocity is small. As the moon is in the proximity of the Earth as seen from the Sun, the moon has the same amount of heat per unit area as that of the Earth. The air molecules have large range of speeds. Even though the r speed of the air molecules is smaller than the escape velocity on the moon, a significant number of molecules have speed greater than escape velocity and they escape. Now rest of the molecules arrange the speed distribution for the equilibrium temperature. Again a significant number of molecules escape as their speeds exceed escape speed. Hence, over a long time the moon has lost most of its atmosphere.

At

for

(b) As the molecules move higher their potential energy increases and hence kinetic energy decreases and hence temperature reduces.

At greater height more volume is available and gas expands and hence some cooling takes place.

Question 28:

Consider an ideal gas with following distribution of speeds.

Distribution of Speeds
Speed (m/s) of molecules
200

400

600

800

1000

10

20

40

20

10

(i) Calculate and hence

(ii) If all the molecules with speed escape from the system, calculate new and hence T.

Answer:

(This problem is designed to give an idea about cooling by evaporation)

(i)

(ii)

Question 29:

Ten small planes are flying at a speed of in total darkness in an air space that is 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 safety region around the plane can be approximated by a sphere of radius .

Answer:

Time

Question 30:

A box of is filled with nitrogen at at . The box has a hole of an area . How much time is required for the pressure to reduce by , if the pressure outside is .

Answer:

speed of molecule inside the box along direction

number of molecules per unit volume

In time , particles moving along the wall will collide if they are

within distance. Let area of the wall. No. of particles colliding in time (factor of due to motion towards wall) .

In general, gas is in equilibrium as the wall is very large as compared to hole.

No. of particles colliding in time If particles collide along hole, they move out. Similarly outer particles colliding along hole will move in.

Net particle flow in time as temperature is same in and out.

After some time pressure changes to inside

no. of particle gone put

Question 31:

Consider a rectangular block of wood moving with a velocity in a gas at temperature and mass density . Assume the velocity is along x-axis and the area of cross-section of the block perpendicular to is A. Show that the drag force on the block is , where m is the mass of the gas molecule.

Answer:

. of molecules per unit volume

speed of gas molecules

When block is moving with speed , relative speed of molecules w. r. t. front face

Coming head on, momentum transferred to block per collision

Where of molecule.

No. of collision in time where area of cross section of block and factor of appears due to particles moving towards block.

Momentum transferred in time form front surface

Similarly momentum transferred in time from back surface

Net force (drag force) form front

We also have

Therefore,

Thus drag