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NCERT Exemplar Class 11 Physics Solutions Chapter 13 Kinetic Theory

NCERT Exemplar Class 11 Physics Solutions Chapter 13 Kinetic Theory

Edited By Vishal kumar | Updated on Apr 09, 2025 01:42 PM IST

Did you know gas molecules are always moving and bumping into each other—even if we can't see them? This chapter helps you understand how gases really work and what’s going on inside things like balloons and tyres!

Chapter 13 – Kinetic Theory is about understanding how gases behave and how their molecules move around. You’ll explore both the big-picture (macroscopic) view and the tiny-particle (microscopic) view of gases. At first, the chapter might feel a bit tricky, but with the help of NCERT Exemplar Class 11 Physics Chapter 13 Solutions, it becomes much easier to understand and remember.

This Story also Contains
  1. NCERT Exemplar Class 11 Physics Solutions Chapter 13: MCQ I
  2. NCERT Exemplar Class 11 Physics Solutions Chapter 13: MCQII
  3. NCERT Exemplar Class 11 Physics Solutions Chapter 13: Very Short Answer
  4. NCERT Exemplar Class 11 Physics Solutions Chapter 13: Short Answer
  5. NCERT Exemplar Class 11 Physics Solutions Chapter 13: Long Answer
  6. Topics in NCERT Exemplar Class 11 Physics Solutions Chapter 13
  7. What will The Student Learn from NCERT Exemplar Class 11 Physics Solutions Chapter 13 Kinetic Theory Of Gases?
  8. NCERT Exemplar Class 11 Physics Solutions Chapter-Wise
  9. NCERT Exemplar Class 11th Solutions
NCERT Exemplar Class 11 Physics Solutions Chapter 13 Kinetic Theory
NCERT Exemplar Class 11 Physics Solutions Chapter 13 Kinetic Theory

The chapter covers kinetic theory of gases, the laws of ideal gases, important postulates and assumptions, and why real gases sometimes don’t behave as expected (non-ideal behavior). It also covers how temperature, pressure, and energy affect gas molecules moving in a container.

NCERT Exemplar Class 11 Physics Solutions Chapter 13: MCQ I

Question:13.1

A cubic vessel (with face horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500ms1 in the vertical direction. The pressure of the gas inside the vessel as observed by us on the ground
(a) remains the same because 500ms1 is very much smaller than vrms of the gas.
(b) remains the same because the motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls.
(c) will increase by a factor equal to(v2rms+(500)2)v2rms where vrms was the original mean square velocity of the gas.
(d) will be different on the top wall and bottom wall of the vessel.

Answer:

The answer is option (b)
In the rocket, the relative velocity of molecules does not change with respect to walls of a container as the mass of a molecule when compared to that of the whole system is negligible. So, the whole gas system moves as a single unit. The rocket moves at a constant speed which makes the acceleration zero, and hence the pressure remains the same as observed by us inside the gas vessel.

Question:13.2

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 that totally absorbs any gas molecule incident on it. At any given time,
(a) The pressure on EFGH would be zero
(b) The pressure on all the faces will be equal
(c) The pressure of EFGH would be double the pressure on ABCD
(d) The pressure on EFGH would be half that on ABCD

Answer:

The answer is option (d)
The rate of transfer of momentum on the wall exerts pressure on the wall due to the force exerted by the molecules. Elastic collision takes place, and hence, the molecules bounce back. The walls absorb the magnitude of momentum transferred to it by each molecule, which is equal to 2mv. So, the net rate of change of momentum is mv, and the pressure of EFGH is halved compared to ABCD.

Question:13.3

Boyle’s law is applicable for an
(a) adiabatic process
(b) isothermal process
(c) isobaric process
(d) isochoric process

Answer:

The answer is the option (b)
At constant temperature, Boyle’s law is applicable
PV=nRT (n, R, T are constant in this case)
So, PV = constant and P1V

Question:13.4

A cylinder containing an ideal gas is in a 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
(a) both P and V of the gas will change
(b) the only P will increase according to Charles’ law
(c) V will change but not P
(d) P will change but not V
Ideal Gas Cylinder

Answer:

The answer is option (c)
In case of an ideal gas, the pressure remains the same throughout irrespective of the initial or final position. Here, P=MgA and no friction acts on piston and the cylinder
We have, PV=nRT
Since, P, n and R, are constant here, VT. So, the temperature increases as volume increases and vice-versa at the same time, when pressure remains constant.

Question:13.5

Volume versus temperature graphs for a given mass of an ideal gas is shown in the figure. At two different values of constant pressure. What can be inferred about the relation between P1 and P2?
Volume vs Temperature graph
(a)P1>P2
(b) P1=P2
(c) P1<P2
(d) Data is insufficient

Answer:

The answer is the option (a)

The pressure and quantity of gas are constant here.
From PV=nRT, we can say that, VT
So, V1T1 = constant (slope = constant)
V=nRTP
dVdT=nRP
hence its value decreases with pressure, so, dVdT1P
so, slope of P1 is smaller than P2 and hence a is the right option.

Question:13.6

1 mole of H2 gas is contained in a box of volume V=1.00m3 at T = 300 K. The gas is heated to a temperature of T= 3000 K, and the gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal)
(a) same as the pressure initially
(b) 2 times the pressure initially
(c) 10 times the pressure initially
(d) 20 times the pressure initially

Answer:

The answer is option (d)
The transfer of the rate of change of momentum by the particles to the walls is what causes the exertion of pressure by the gas. As temperature rises and hydrogen molecules break into atoms, the mass of the particle becomes halved, and the number of particles becomes double. Since the velocity is strictly dependent on the temperature, at the same temperature, i.e., at 300K, the velocity of particles of H2 as well as H remains the same. Also, the pressure does not change as the atomic form changes since the rate of transfer of momentum is also the same in the case of H2 as well as H.

Question:13.7

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, and similarly for oxygen. Then,
(a) f1(v)+f2(v)=f(v) obeys the Maxwell’s distribution law
(b) f1(v),f2(v) will obey the Maxwell’s distribution law separately
(c) neither f1(v)norf2(v)will obey Maxwell’s distribution law
(d) f1(v)andf2(v)will be the same

Answer:

The correct answer is option (b)
F1(v): speed of n molecules = (v+dv)
The number of molecules remains the same, which is one mole for f1(v)andf2(v). Since the molecules differ in mass, they will also differ in speed, and hence, both gases will separately obey Maxwell’s distribution.

Question:13.8

An inflated rubber balloon contains one mole of an ideal gas and 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
(a) 1.1 P
(b) P
(c) less than P
(d) between P and 1.1

Answer:

The correct answer is option (d)
According to the ideal gas equation, PV = nRT
Here, PVT = constant.
P1V1T1=P2V2T2
So, P2=1.11.05(p)=(1.0476)(p)
So, the value of P2 is between p and 1.1 p and hence, option d is correct.

NCERT Exemplar Class 11 Physics Solutions Chapter 13: MCQII

Question:13.9

ABCDEFGH is a hollow cube made of an insulator (figure) Face ABCD has a positive charge on it. Inside the cube, we have ionised hydrogen.
The usual kinetic theory expression for pressure
(a) will be valid
(b) will not be valid since the ions would experience forces other than due to collisions with the walls
(c) will not be valid since collisions with walls would not be elastic
(d) will not be valid because isotropy is lost

Answer:

The correct answer is option (b) and (d)
The wall of ABCD is positively charged. The presence of hydrogen ions and the charge on the walls lead to an electrostatic force which acts in contrast to the collision and makes the kinetic theory of gases invalid in this case. The isotropy also gets lost given the presence of hydrogen ions instead of hydrogen molecules. Hence, options b and d are correct.

Question:13.10

Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory PV=23E, E is
(a) the total energy per unit volume
(b) only the translational part of energy because rotational energy is very small compared to the translational energy
(c) only the translational part of the energy because during collisions with the wall, pressure relates to change in linear momentum
(d) 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

Answer:

The correct answer is option (c)
As per the kinetic theory of gases, the perpendicular forces exerted by the molecules on the walls while in motion are only responsible for the pressure exerted due to the gas molecules. So, for molecules striking at angles other than 90 degrees, no pressure will be exerted. Hence, in this case, only translational motion change leads to pressure on the wall. So, PV=23E, which represents the translational motion part and hence c is the correct option.

Question:13.11

In a diatomic molecule, the rotational energy at a given temperature
(a) obeys Maxwell’s distribution
(b) have the same value for all molecules
(c) equals the translational kinetic energy for each molecule
(d) is (23)rd the translational kinetic energy for each molecule

Answer:

The correct answer is the options (a) and (d)
If we assume a diatomic molecule along the z-axis, its energy along that axis will be zero. The total energy of a diatomic molecule can be expressed as: E=12mvx2+12mvy2+12mvz2+12IxWx2+12IxWy2
The number of independent terms in the expression =5. The above expression obeys Maxwell’s distribution as their velocities can be predicted with Maxwell’s findings. In this case, for each molecule, 3 translational and 2 rotational energies are associated. So, at any temperature, rotational energy = (23)rd translational KE

Question:13.12

Which of the following diagrams (figure) depicts ideal gas behavior?
Ideal Gas Graphs

Answer:

The correct answer is options (a) and (c)
a) PV=nRT
where R and T are constant.
Since P is constant, VTas given in the graph of option a.
Hence, the option is correct.
c) In case where V = constant
PT, which is a straight line. Hence, option c is correct.

Question:10.13

When an ideal gas is compressed adiabatically, its temperature rises, and the molecules on the average have more kinetic energy than before. The kinetic energy increases,
(a) because of collisions with moving parts of the wall only
(b) because of collisions with the entire wall
(c) because the molecules get accelerated in their motion inside the volume
(d) because of the redistribution of energy amongst the molecules

Answer:

The correct answer is option (a)
The number of collisions per second between the molecules and walls increases, and the mean free path becomes smaller as an ideal gas is compressed. This, in turn, increases the temperature of the gas, which increases the overall kinetic energy of the gas molecules as KE depends on the temperature.

NCERT Exemplar Class 11 Physics Solutions Chapter 13: Very Short Answer

Question:13.14

Calculate the number of atoms in 39.4 g of gold. The molar mass of gold is 197 g mole-1.

Answer:

Number of atoms on 197 g gold = 6.023×1023
Number of atoms in 1g of gold, n
=6.023×1023197
Hence, the number of atoms in 34g of gold =
34×(6.023×1023197)=1.2×1023 atoms

Question:13.15

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

Answer:

Let, P1 = 1 atm, P2 = 1 atm, V1 =100cc, V2 = ?T1 =300K, T2 =600K
From the ideal gas equation, we have
P1V1T1=P2V2T2
Hence,
V2=100×600300=200cc

Question:13.16

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

Answer:

V1 rms =100m/s, T1=300K, T2 =400K, V2 rms =?
We know that,
Vrms=3RTm
VrmsT
Hence,
V1rmsV2rms=T1T2
100V2rms=300400
V2rms=115.4ms

Question:13.17

Two molecules of a gas have speeds of 9×1016ms1 and 1×1016ms1 respectively. What is the root mean square speed of these molecules?

Answer:

Vrms=V12+V22...........Vn2n
We know that, V1=9×1016ms1 and V2=1×1016ms1
Hence, Vrms=(9×106)2+(1×106)22
Vrms=106×822=6.4×106m/s

Question:13.18

A gas mixture consists of 2.0 moIes 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.)

Answer:

Degree of freedom is necessary to be known if we need to find the total energy of a particular molecule.
An oxygen molecule has 2 atoms, so the degree of freedom = 2 rotational + 3 translational = 5
Total internal energy for 2 moles of oxygen = 2×52RT=5RT
Neon gas has a degree of freedom equal to 3, since it is a monoatomic gas-only translational degree of freedom is present. So, the total internal energy =32RT per mole.
For 4 moles of neon gas, total internal energy = 4×32RT=6RT
Hence total internal energy of 2 moles oxygen + 4 moles Neon = 5 + 6 = 11 RT

Question:13.19

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.

Answer:

Mean free path formula, λ=12πd2n
Here, n = number of molecules per unit volume. In our case, n will be constant.
Here, d = diameter of molecules.
Now, λ1d2
So,λ1λ2=d22d12=41
Hence, λ1:λ2=4:1

NCERT Exemplar Class 11 Physics Solutions Chapter 13: Short Answer

Question:13.20

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.

V1V2
μ1μ2
p1p2

Answer:

According to the ideal gas situation, we have PV = nRT
For chamber 1 and chamber 2,
P1V1=n1RT1 and P2V2=n2RT2
P1=1atm,P2=2atm,V1=2L,V2=3L
T1=T,T2=T,n1=4,n2=5
When we remove the partition, n=n1+n2 and V=V1+V2
According to kinetic theory, Translational gas kinetic energy=PV=23. E per mole
So, the translational KE for both cases will be,
P1V1=23.n1E1 and P2V2=23.n2E2
Adding, P1V1+P2V2=23.n1E1+23.n2E2
n1E1+n2E2=32(P1V1+P2V2)
hence by combining the results we get,
P(V1+V2)=23[32(P1V1+P2V2)]
P=P1V1+P2V2V1+V2=1.6atm

Question:13.21

A gas mixture consists of molecules of A, B and C with masses. Rank the three types of molecules in decreasing order of (a) average KE, (b) RMS speeds.

Answer:

Vav=8KbTπm=8RTπm=8PVπm
as the temperature and pressure are equal,
Vav1m
hence, Vc>Vb>Va
now KEV2 and KEm
hence KE in decreasing order will be,
KEc>KEb>KEa
b)
now, Vrms=3KbTm
since it is given that, m(a)>m(b)>m(c)
Vrms(c)>Vrms(b)>Vrms(a)

Question:13.22

We have 0.5 g of hydrogen gas in a cubic chamber of size 3cm 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 considered as spheres of radius 1 A ).

Answer:

The volume of a sphere = the volume of one molecule
=43πr3
Here r=1010m
So, volume = 4×1.05×1030=4.2×1030m3
For 0.5 g of hydrogen gas, no of moles = 0.52=0.25moles
Hence the volume of hydrogen molecules = 0.25×6.023×1023×4.2×1030=6.3×107m3
For a constant temperature, ideal gas à Pi Vi = Pf Vf
Vf=PiViPf=1100×(3×102)3
Hence, Vf=2.7×107m3
The gas here will not obey the ideal gas behaviour as the kinetic energy of the molecules will not interact with each other due to compression.

Question:13.23

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?

Answer:

The volume of a gas is inversely proportional to the pressure of the gas at a constant temperature as stated by Boyle’s law. When air is continuously pumped inside the tyre, the number of moles of gas (i.e. the mass of the gas) increases. Since Boyle’s law is only applicable for a constant mass of gas, it will not hold true in this case.

Question:13.24

A balloon has 5.0 mole of helium at 7C. Calculate
(a) the number of atoms of helium in the balloon.
(b) the total internal energy of the system.

Answer:

Helium gas, n = 5 moles and T = 280 K
a) number of atoms of He = 5×6.023×1023=3.0115×1024 atoms of He
b) the degree of freedom for a helium atom is 3 since it is monoatomic
so, average KE=32KbT per molecule
average KE=32×1.38×1023×80×3.0115×1024
hence total energy = 1.74×104J

Question:13.25

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

Answer:

Degree of freedom of H2 molecule = 3 translational degree of freedom + 2 rotational degree of freedom = 5.
Number of molecules in 1cc of hydrogen gas at NTP à 22.4 L = 22400 cc H2 gasà it has 6.023×1023 molecules
So, 1cc of H2 gas at STP has,6.02322400×1023=2.688×1019 molecules
Hence the total degree of freedom =5×2.688×1019=1.344×1020

Question:13.26

An insulated container containing monoatomic gas of molar mass m is moving with a velocity v0. If the container is suddenly stopped, find the change in temperature.

Answer:

Since the gas is monoatomic, only translational degree of freedom will be applicable. KE per molecule = 32RT. when the container which is insulated has suddenly stopped, a transfer of kinetic energy takes place to the gas molecules. Let ΔT be the slight increase in temperature and n be the number of moles of gas.
The resultant increase in translational KE can be presented as,
KE=32n.R.ΔT
Increased KE due to velocity,
v0=12(mn)v02
Hence,
mn2v02=32n.R.ΔT
So,
ΔT=mnv02×22×3×nR=mv023R

NCERT Exemplar Class 11 Physics Solutions Chapter 13: Long Answer

Question:13.27

Explain why
(a) there is no atmosphere on the moon.
(b) there is a fall in temperature with altitude.

Answer:

a) The acceleration on the moon due to gravity is one-sixth that of Earth
escape velocity on the moon can be written as: Ves=2gR=2.38km/s
mass of hydrogen, m = 1.67 x 10-24 kg
v(rms)=3KbTm=3×1.38×1023×3001.67×1024=2.72km/s
v(RMS) is larger than the escape velocity as the gravitational force is small. The sun-moon distance is fairly equal to that of the earth. The energy of the sun reaches in a larger intensity to the moon due to its lower density of the atmosphere. So, the molecules of sunlight have a larger RMS speed and hence can escape out fairly easily. Hence, the moon has lost its atmosphere over time.
b) The kinetic energy of the air molecule gives the characteristic temperature to the atmosphere. At greater heights, atmospheric pressure is low, which makes air molecules rise higher, which in turn leads to an increase in their potential energy and decrease in their kinetic energy. Since the overall kinetic energy decreases, the temperature also decreases. Also, the lower atmospheric pressure causes expansion of the gas, which also provide a cooling effect.

Question:13.28

Consider an ideal gas with the following distribution of speeds.

Speed% of molecules
20010
40020
60040
80020
100010

(i) Calculate V rms and hence T. (m=3.0×1026kg)
(ii) If all the molecules with speed 1000 m/s escape from the system, calculate new Vrms and hence T.

Answer:

(i)
v2(rms)=10×(200)2+20(400)2+40(600)2+20(800)2+10(1000)210+20+40+20+10=4.08×105

12mv2(rms)=32KbT
T=mv2(rms)3Kb=3×1026×105×4.083×1.38×1023=296K
(ii)
Molecules escape at rate of 1000m/s, we can calculate the v2 (rms) as follows
v2(rms)=10×(200)2+20(400)2+40(600)2+20(800)210+20+40+20
v2(rms)=105[1×4+2×16+4×36+2×64]90
v(rms)=1003308585m/s
T=13(mv2(rms)Kb)=3×1026×(585)23×1.28×1023=284.04K

Question:13.29

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 safety region around the plane can be approximated by a sphere of radius 10m.

Answer:

The motion of molecules in a confined space can be considered a plane. Mean free path λ can be considered as distance travelled by molecules between two planes to avoid any collision, time = distance/speed
=λv=12nπd2.v
Number of particles per unit volume V = N/volume
N=1020×20×1.5km3=0.0167km3
d=2×10=20m=150km/hr
so, time
=12nπd2.V=11.414×0.0167×3.14×20×20×106×150=225hours.

Question:13.3

A box of 1.00m3 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.

Answer:

Let v1 = volume of box = 1 m3
Let p1 be the initial pressure = 1.5 atm
Let p2’ be the final pressure =1.5 - 0.1 = 1.4 atm
t1 = initial temperature = 300K, t2 = final temperature = 300 K
let a be the area of hole = 108m2
The pressure difference initially between the tyre and atmosphere, ΔP = (1.5 -1) = 0.5 atm
Mass of N2 molecule
=0.0286.023×1023=46.5×1027kg
Kb=1.38×1023
Now since
|vix|=|viy|=|viz|
Hence, vrms2=3vix2
For a gas molecule, Kinetic energy = 32KbT
Now,
12mv2=3vix2
vix=KbTm (A)
The N2 molecules striking the wall in time Δt outwards
12Pn1KbTm (A) outwards.
The temperature of the air and inside the box is equal to T.
The N2 molecules striking the wall in time Δt inwards = 12Pn2KbTm (A) inwards.
Here, Pn2 = density of air molecules
So, we can calculate the net number of molecules going outward as:
12[Pn1Pn2]KbTm(A)Δt
We know that,PV=nRT,n=PVRT
Pn1 = total number of molecules in the box/ volume of the box
=nNaV=PNaRT per unit volume.
After a time, T, the pressure reduces to (1.5-0.1) = 1.4 atm = P’2
The new density of the Na molecules =Pn1=P2NaRT per unit volume.
The number of molecules going out from volume V=(P1P1)v=P1NaRT(V)P2NaRT(V)
= NaVRT[P1P2] where P’2 = final pressure of the box
The total number of molecules which exit the hole in time t’ is:
12[Pn1Pn2]KbTmt(A)
Pn1Pn2=P1NaRTP2NaRT=NaRT[P1P2]
The net number of molecules exiting in time t' is
Na2RT[P1P2]KbTmt(A)
Now we can write from the above results,
t=2(P1P2)(P1P2).(Va).mKbT
t=2[1.51.4][1.51].1108.46.5×10271.38×1023×300
t=0.4×108775×10669
t=0.4×105×3.35=1.34×105seconds.

Question:13.31

Consider a rectangular block of wood moving with a velocity v0 in gas at temperature T and mass density ρ . Assume the velocity is along the 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 4ρAv0KTm, where m is the mass of the gas molecule.

Answer:

We assume ‘p’ to be the number of molecules per unit volume. Hence ‘p’ is the per unit volume molecular density. Let v be the velocity of gas molecules.
The molecules of the gas strike the front face and the back face of the box when it moves. The back face relative velocity = (vv0)
Change in momentum on the front face of the box = 2m(v+v0) and the change in momentum on the back face of the box = 2m(vv0).
Nf =Total number of molecules striking the box’s front face = 12[A.(v+v0)Δt]p
Nf=12(v+v0)A.p.Δt
Nb = Total number of molecules striking the box’s back face
=12[A.(v+v0)Δt]p
Nb
=12(v+v0)A.p.Δt
Total change in momentum at the front face can be calculated s below:
Pf=2m(v+v0)×Nf=2m(v+v0)×12(v+vo)A.p.Δt
Pf=m(v+v0)2A.p.Δt in the backward direction.
Force on front end = Ff = Pf = m(v+v0)2A.p in the backward direction
In the same way, the force on the back face, Fb = +m(vv0)2A.p
So, the net force can be calculated as:
m(v+v0)2A.p+m(vv0)2A.p
It can be expanded and simplified as,
=mAp4v.v0
The magnitude of dragging force= 4mv.v0.A.p
Kinetic energy for a molecule of gas can be calculated as:
KE=12mv2=32KbT
Hence, v=KbTm
So, we can write the drag force as 4m.A.p.voKbTm

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Topics in NCERT Exemplar Class 11 Physics Solutions Chapter 13

NCERT Exemplar Class 11 Physics Chapter 13 – Kinetic Theory of Gases covers important topics like the behaviour of gases, ideal gas laws, kinetic theory postulates, and non-ideal gas behaviour. It also explains how temperature, pressure, and molecular motion are all connected. These topics help build a strong base for both exams and a real-world understanding of gases.

What will The Student Learn from NCERT Exemplar Class 11 Physics Solutions Chapter 13 Kinetic Theory Of Gases?

The Kinetic Theory of Gases chapter is based on a cool idea: gas molecules are super tiny and far apart, and they keep moving around randomly, bouncing off each other and the container walls. This random movement—affected by temperature, pressure, and other factors—helps explain the physical properties of gases. In this chapter, you’ll learn about the kinetic theory and its postulates and assumptions (like gases are made of particles, particles have no volume, and they don’t attract or repel each other). There are about 9 main assumptions to understand.

Important Topics To Cover From NCERT Exemplar Class 11 Physics Solutions Chapter 13 Kinetic Theory Of Gases

Here are some important topics you should focus on from NCERT Exemplar Class 11 Physics Chapter 13 – Kinetic Theory of Gases:

  • Postulates and assumptions of kinetic theory (like gas particles have zero volume and no forces between them).

  • All the major gas laws – Boyle’s law, Charles’s law, Avogadro’s law, and Graham’s law of diffusion.

  • Concepts of pressure, temperature, and molecular motion and how they relate.

  • The ideal gas equation and the difference between ideal and real gases.

  • Maxwell-Boltzmann distribution law – how gas particles are spread based on energy and velocity (important for exams!).

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NCERT Exemplar Class 11 Physics Solutions Chapter-Wise

NCERT Exemplar Class 11th Solutions

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Frequently Asked Questions (FAQs)

1. What are the benefits of these solutions?

Our solutions are detailed and created most exhaustively, and this will help in understanding the topic, solving questions, and is also learning how to answer questions in the exam.

2. Are these solutions as per the CBSE pattern?

Yes, these NCERT exemplar class 11 physics solutions chapter 13 are as per the CBSE pattern, as they are solved step by step and according to the marking scheme.

3. Is this chapter important for exams like JEE and NEET?

Yes, it builds strong basics about gases, the motion of molecules, and gas laws—topics that are often asked in competitive exams.

4. What are the key assumptions of the kinetic theory?

Some important ones include the following: gas is made of particles, they have negligible volume, there are no forces between them, and they move randomly in all directions.

5. What is the kinetic theory of gases?

It's a theory that explains the behaviour of gases by assuming they are made of tiny, fast-moving particles (molecules) that collide with each other and the container walls.

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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