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    NCERT Exemplar Class 11 Physics Solutions Chapter 13 Kinetic Theory

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    NCERT Exemplar Class 11 Physics Solutions Chapter 13 Kinetic Theory

    Edited By Safeer PP | Updated on Aug 09, 2022 12:21 PM IST

    In chapter 13, the Kinetic Theory of Gases is dealt with. In this chapter, the learners will come to know about the gases, their molecular movement, and how these phenomenons can be understood at both macroscopic and microscopic levels. This chapter can seem to be a bit complicated for the students in the beginning. But if one focuses on the terminology, the processes, and their applications step by step alongside NCERT exemplar Class 11 Physics solutions chapter 13 it will become easier to retain. In this chapter, the students are taught about the kinetic theory gases, gas laws of ideal gases, postulates, assumptions, and the non-ideal gas behavior. This chapter and NCERT exemplar Class 11 Physics chapter 13 solutions encapsulate all the topics related to gas molecule movement in a container along with the factors of temperature, pressure, and energy.

    NCERT Exemplar Class 11 Physics Solutions Chapter 13-MCQI

    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 500 ms^{-1} in the vertical direction. The pressure of the gas inside the vessel as observed by us on the ground
    (a) remains the same because 500 ms^{-1} 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\frac{\left ( v^{2}rms +\left ( 500 \right )^{2} \right )}{v^{2}rms} 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 the 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 which 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 the 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 as 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 P\propto \frac{1}{V}

    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

    Answer:

    The answer is the option (c)
    In case of an ideal gas, the pressure remains the same throughout irrespective of the initial or final position. Here, P= \frac{Mg}{A} and no friction acts on piston and the cylinder
    We have, PV = nRT
    Since, P, n and R, are constant here, V\propto T. 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 P_{1} and P_{2}?

    (a)P_{1}>P_{2}
    (b) P_{1}=P_{2}
    (c) P_{1}<P_{2}
    (d) Data is insufficient

    Answer:

    The answer is the option (a)

    Pressure and quantity of gas are constant here.
    From PV = nRT, we can say that, V \propto T
    So, \frac{V_{1}}{T_{1}} = constant (slope = constant)
    V = \frac{nRT}{P}
    \frac{dV}{dT}=n \frac{R}{P}
    hence its value decreases with pressure, so, \frac{dV}{dT}\propto \frac{1}{P}
    so, slope of P_{1} is smaller than P_{2} and hence a is the right option.

    Question:13.6

    1 mole of H_{2} gas is contained in a box of volume V = 1.00 m^3 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 the option (d)
    The transfer of the rate of change of momentum by the particles to the walls is what causes 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 H_{2} 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 same in the case of H_{2} 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 f_{1}(v)dv denotes the fraction of molecules with speed between v and (v + dv) with f_2(v)dv, similarly for oxygen. Then,
    (a) f_{1}(v) + f_{2}(v) = f (v) obeys the Maxwell’s distribution law
    (b) f_{1}(v) , f_{2}(v) will obey the Maxwell’s distribution law separately
    (c) neither f_{1}(v) nor f_{2}(v)will obey Maxwell’s distribution law
    (d) f_{1}(v) and f_{2}(v)will be the same

    Answer:

    The correct answer is the option (b)
    F1(v): speed of n molecules = (v+dv)
    The number of molecules remains the same, which is one mole for f_{1}(v) and f_{2}(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, 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 the option (d)
    According to ideal gas equation, PV = nRT
    Here, \frac{PV}{T} = constant.
    \frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}
    So, P_{2}= \frac{1.1}{1.05}(p)=(1.0476)(p)
    So, the value of P_{2} 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 the 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 make 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 = \frac{2}{3}E, 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 the 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 = \frac{2}{3}E, 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 \left (\frac{2}{3} \right ){rd} the translational kinetic energy for each molecule

    Answer:

    The correct answer is the option (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 = \frac{1}{2} mvx^{2} + \frac{1}{2} mvy^{2} + \frac{1}{2} mvz^{2} + \frac{1}{2} IxWx^{2} + \frac{1}{2} IxWy^{2}
    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 = \left (\frac{2}{3} \right ){rd} translational KE

    Question:13.12

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

    Answer:

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

    Question:10.13

    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,
    (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 the 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 compressed. This, in turn, increases the temperature of the gas, which increased 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 gold. The molar mass of gold is 197 g mole-1.

    Answer:

    Number of atoms on 197 g gold = 6.023 \times 10^{23}
    Number of atoms in 1g of gold, n
    =6.023 \times \frac{10^{23}}{197}
    Hence, number of atoms in 34g of gold =
    34 \times \left (6.023 \times \frac{10^{23}}{197} \right ) = 1.2 \times 10^{23} atoms

    Question:13.15

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

    Answer:

    Let, P_{1} = 1 atm, P_{2} = 1 atm, V_{1} = 100cc, V_{2} = ?T_{1} = 300K, T_{2} = 600K
    From the ideal gas equation, we have
    \frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}
    Hence,
    V_{2} = \frac{100 \times 600}{300}= 200 cc

    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\times \frac{5}{2} RT = 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 = \frac{3}{2} RT per mole.
    For 4 moles of neon gas, total internal energy = 4\times \frac{3}{2} RT = 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, \lambda =\frac{1}{\sqrt{2}}\pi d^{2}n
    Here, n = number of molecules per unit volume. In our case, n will be constant.
    Here, d = diameter of molecules.
    Now, \lambda \propto \frac{1}{d^{2}}
    So,\frac{\lambda _{1}}{\lambda _{2}}=\frac{d_2^{2}}{d_1^{2}}=\frac{4}{1}
    Hence, \lambda _{1}:\lambda _{2}=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 \mu _{1}=4.0 and \mu _{2}=5.0 moles of a gas at pressures p_{1} = 1.00 atm and p_{2} = 2.00 atm. Calculate the pressure after the partition is removed and the mixture attains equilibrium.

    V_{1}V_{2}
    \mu_{1}\mu_{2}
    p_{1}p_{2}

    Answer:

    According to the ideal gas situation, we have PV = nRT
    For chamber 1 and chamber 2,
    P_{1}V_{1} = n_{1}RT_{1} and P_{2}V_{2} = n_{2}RT_{2}
    P_{1}=1atm, P_{2}=2 atm, V_{1}=2L, V_{2}=3L
    T_{1}=T, T_{2}=T, n_{1}=4, n_{2}=5
    When we remove the partition, n = n_{1}+n_{2} and V = V_{1} + V_{2}
    According to kinetic theory, Translational gas kinetic energy=PV = \frac{2}{3}. E per mole
    So, the translational KE for both cases will be,
    P_{1}V_{1} = \frac{2}{3}. n_{1} E_{1} and P_{2}V_{2} = \frac{2}{3}. n_{2} E_{2}
    Adding, P_{1}V_{1}+P_{2}V_{2} =\frac{2}{3}. n_{1} E_{1}+ \frac{2}{3}. n_{2} E_{2}
    n_{1}E_{1}+n_{2}E_{2}=\frac{3}{2}\left ( P_{1}V_{1}+P_{2} V_{2} \right )
    hence by combining the results we get,
    P(V_{1}+V_{2}) = \frac{2}{3}\left [ \frac{3}{2}(P_{1}V_{1}+P_{2}V_{2}) \right ]
    P = \frac{P_1V_1 + P_{2}V_2}{V_{1} + V_{2}} = 1.6 atm

    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 =\sqrt{\frac{8 K_bT}{\pi m}} = \sqrt{\frac{8RT}{\pi m}} = \sqrt{\frac{8PV}{\pi m}}
    as the temperature and pressure are equal,
    Vav\propto \frac{1}{\sqrt{m}}
    hence, Vc > Vb > Va
    now KE \propto V^2 and KE \propto m
    hence KE in decreasing order will be,
    KE c > KE b > KE a
    b)
    now, V_{rms} =\sqrt{\frac{3K_bT}{m}}
    since it is given that, m(a) > m(b) > m(c)
    V_ {rms} (c) > V_{ rms} (b) > V_{ rms} (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
    =\frac{4}{3}\pi r^{3}
    Here r= 10^{-10} m
    So, volume = 4 \times 1.05 \times 10^{-30} = 4.2 \times 10^{-30} m^{3}
    For 0.5 g of hydrogen gas, no of moles = \frac{0.5}{2}=0.25 moles
    Hence the volume of hydrogen molecules = 0.25 \times 6.023 \times 10^{23} \times 4.2 \times 10^{-30} = 6.3 \times 10^{-7} m^{3}
    For a constant temperature, ideal gas à Pi Vi = Pf Vf
    Vf =\frac{P_i V_i}{P_f} = \frac{1}{100}\times (3\times 10^{-2})^{3}
    Hence, V_f = 2.7 \times 10^{-7} m^{3}
    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 7^{\circ}C. 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 \times 6.023 \times 10^{23} = 3.0115 \times 10^{24} atoms of He
    b) the degree of freedom for a helium atom is 3 since it is monoatomic
    so, average KE =\frac{3}{2}K_bT per molecule
    average KE = \frac{3}{2} \times 1.38 \times 10^{-23} \times 80 \times 3.0115 \times 10^{24}
    hence total energy = 1.74 \times 10^{ 4 }J

    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 \times 10^{23} molecules
    So, 1cc of H2 gas at STP has,\frac{ 6.023}{22400}\times 10^{23} = 2.688 \times 10^{19} molecules
    Hence the total degree of freedom =5 \times 2.688 \times 10^{19 }= 1.344 \times 10^{20}

    Question:13.26

    An insulated container containing monoatomic gas of molar mass m is moving with a velocity v_{0}. 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 = \frac{3}{2} R T. when the container which is insulated has suddenly stopped, a transfer of kinetic energy takes place to the gas molecules. Let \Delta T 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 = \frac{3}{2} n. R. \Delta T
    Increased KE due to velocity,
    v_{0} = \frac{1}{2} (m n) v_{0}^{2}
    Hence,
    \frac{mn}{2} v_{0}^{2}=\frac{3}{2} n. R. \Delta T
    So,
    \Delta T = \frac{m n v_{0}^{2} \times 2}{2 \times 3 \times n R} =\frac{ m v_{0}^{2}}{3R}

    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: V es = \sqrt{2gR} = 2.38 km/s
    mass of hydrogen, m = 1.67 x 10-24 kg
    v (rms) =\sqrt{ \frac{3 Kb T}{m}} = \sqrt{\frac{3 \times 1.38 \times 10^{-23}\times 300}{1.67 \times 10^{-24}}} = 2.72 km/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 \times 10^{-26} kg)
    (ii) If all the molecules with speed 1000 m/s escape from the system, calculate new Vrms and hence T.

    Answer:

    (i)
    \\v^{2} (rms) = \frac{10 \times (200)^{2} + 20(400)^{2} + 40(600)^{2} + 20(800)^{2} + 10(1000)^{2}}{10+20+40+20+10}\\=4.08\times10^{5}

    \frac{1}{2}m v^{2} (rms)=\frac{3}{2} Kb T
    T = \frac{m v^{2} (rms)}{3 Kb} = \frac{3 \times 10^{-26} \times 10^{5} \times 4.08}{3\times 1.38\times 10^{-23}} = 296K
    (ii)
    Molecules escape at rate of 1000m/s, we can calculate the v2 (rms) as follows
    v^{2} (rms) = \frac{10 \times (200)^{2} + 20(400)^{2} + 40(600)^{2} + 20(800)^{2}}{10+20+40+20}
    v^2 (rms) = \frac{105[1\times 4 + 2 \times 16 + 4 \times 36 + 2 \times 64]}{90}
    v(rms) = \frac{100}{3}\sqrt{ 308} \sim 585 m/s
    T = \frac{1}{3} (\frac{m v^{2} (rms)}{Kb}) = \frac{3 \times 10-26 \times (585)2}{3 \times 1.28 \times 10^{-23}} = 284.04 K

    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 = 10 ^{-8} m^{2}
    The pressure difference initially between the tyre and atmosphere, ΔP = (1.5 -1) = 0.5 atm
    Mass of N2 molecule
    =\frac{0.028}{6.023 \times 10^{23}} = 46.5 \times 10^{-27} kg
    Kb = 1.38 \times 10^{-23}
    Now since
    |v_{ix}|= | v_{iy} |= \left |v_{iz} \right |
    Hence, v^2_{rms} = 3v_{ix}^2
    For a gas molecule, Kinetic energy = \frac{3}{2}KbT
    Now,
    \frac{1}{2}mv^{2} = 3v_{ix}^{2}
    v_{ix }= \sqrt{\frac{Kb T}{m}} (A)
    The N2 molecules striking the wall in time \Delta t outwards
    \frac{1}{2} P_{n1} \sqrt{\frac{Kb T}{m}} (A) outwards.
    The temperature of the air and inside the box is equal to T.
    The N2 molecules striking the wall in time \Delta t inwards = \frac{1}{2} P_{n2} \sqrt{\frac{Kb T}{m}} (A) inwards.
    Here, Pn2 = density of air molecules
    So, we can calculate the net number of molecules going outward as:
    \frac{1}{2} \left [ P_{n1}-P_{n2} \right ] \sqrt{\frac{K_b T}{m}}(A)\Delta t
    We know that,PV = nRT, n= \frac{PV}{RT}
    Pn1 = total number of molecules in the box/ volume of the box
    =\frac{nNa}{V}= \frac{PNa}{RT} 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 =P^{'}n1 = \frac{P2^{'}Na}{RT} per unit volume.
    The number of molecules going out from volume V = (P1 - P^{'}1) v = \frac{P1Na}{RT} (V) -\frac{ P2Na}{RT}(V)
    = \frac{Na V}{RT} [P1 - P^{'}2] where P’2 = final pressure of the box
    The total number of molecules which exit the hole in time t’ is:
    \frac{1}{2}[Pn1 - Pn2] \sqrt{\frac{Kb T}{m t^{'}}} (A)
    Pn1 - Pn2 = \frac{P1Na}{RT} -\frac{ P2Na}{RT}= \frac{Na}{RT} [P1-P2]
    The net number of molecules exiting in time t' is
    \frac{Na}{2RT} [P1 - P2] \sqrt{\frac{Kb T}{m t^{'}}} (A)
    Now we can write from the above results,
    t^{'} = 2\frac{(P_1 - P^{'}_2)}{(P_1-P_2)}. \left ( \frac{V}{a} \right ).\sqrt{ \frac{m}{Kb T}}
    t^{'} = \frac{2[1.5-1.4]}{ [1.5-1]}.\frac{1}{10^{-8}}. \sqrt{\frac{46.5 \times 10^{-27}}{1.38 \times 10^{-23}\times 300} }
    t^{'}= 0.4 \times 10^{8}\sqrt{ \frac{775 \times 10^{-6}}{69}}
    t^{'} = 0.4 \times 10^{5} \times 3.35 = 1.34 \times 10^{5}seconds.

    Question:13.31

    Consider a rectangular block of wood moving with a velocity v0 in gas at temperature T and mass density \rho . Assume the velocity is along the x-axis and the area of cross-section of the block perpendicular to v_{0} is A. Show that the drag force on the block is 4\rho Av_{0}\sqrt{\frac{KT}{m}}, 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 = (v-v_0)
    Change in momentum on the front face of the box = 2m(v+v_{0}) and the change in momentum on the back face of the box = 2m(v-v _0).
    Nf =Total number of molecules striking the box’s front face = \frac{1}{2}[A.(v+v_{0}) \Delta t] p
    Nf = \frac{1}{2}(v+v_{0}) A.p. \Delta t
    Nb = Total number of molecules striking the box’s back face
    =\frac{1}{2}[A.(v+v_{0}) \Delta t] p
    Nb
    =\frac{1}{2}(v+v_{0}) A.p. \Delta t
    Total change in momentum at the front face can be calculated s below:
    Pf = 2m(v+v_{0}) \times Nf = 2m(v+v_{0}) \times \frac{1}{2}(v+v_{o}) A.p. \Delta t
    Pf = - m(v+v_0)2 A.p. \Delta t in the backward direction.
    Force on front end = Ff = Pf = - m(v+v_0)2 A. p in the backward direction
    In the same way, the force on the back face, Fb = + m(v-v_{0})2 A. p
    So, the net force can be calculated as:
    - m(v+v_{0})^{2} A. p+ m(v-v_{0})^{2} A. p
    It can be expanded and simplified as,
    = -m A p 4v.v_{0}
    The magnitude of dragging force= 4m v.v _{0}.A.p
    Kinetic energy for a molecule of gas can be calculated as:
    KE = \frac{1}{2}mv^{2} = \frac{3}{2} Kb T
    Hence, v = \sqrt{\frac{Kb T}{m}}
    So, we can write the drag force as 4m.A. p. v_o \sqrt{\frac{Kb T}{m}}

    NCERT questions are one of the most crucial ones if one wants to score high in their exams and also want to learn better for entrance exams. We have solved all the questions given in the main exercise as per the CBSE pattern and marking scheme. This will help the student learn better keeping in mind how to answer for better scoring. Our NCERT exemplar Class 11 Physics solutions chapter 13 pdf download are also downloadable so that one can access them offline in the PDF format. Simply, click on the given link and it is done.

    Also, Read NCERT Solution subject wise -

    Also, check NCERT Notes subject wise -

    Topics in NCERT Exemplar Class 11 Physics Solutions Chapter 13

    • 1. Introduction
    • 2. Molecular nature of matter
    • 3. Behaviour of gases
    • 4. Kinetic theory of ideal gases
    • 5. Law of equipartition of energy
    • 6. Specific heat capacity
    • 7. Mean free path

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

    Kinetic theory of gases is the chapter that derives all its topics from the idea that in the gas, the molecules are smaller than the distance between the gas molecules. They move around the container and collide with each other on the walls. Now, this movement of the molecules with the effect of temperature, pressure, and other factors will help in describing the physical properties of the gas. The learner will learn about kinetic theory, its assumptions, and postulates. There are around 9 assumptions like the gas is made of particles, particles have zero volume, there is no interaction between particles, etc.

    Students will also learn about the ideal gas’s gas laws like Avogadro’s law, Amonton’s law, Boyles’ law, Charles law, and Graham's law of diffusion. At the end of the chapter and NCERT exemplar Class 11 Physics chapter 13 solutions the learner will come across the Maxwell and Boltzmann energy and velocity distribution law, which has a lot of significance from an exam point of view.

    NCERT Exemplar Class 11 Physics Solutions Chapter-Wise


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

    · For a better understanding of the kinetic theory of gases, the first thing that one should pay attention to is the gas laws. 5 gas laws explain how an ideal gas behaves when one factor is kept constant. The formulas of these laws will help in solving numerical based questions in the exam.

    · Secondly, a student should pay attention to non-ideal gas behaviour. In this topic, the real gases are discussed who do not follow the ideal gas behaviour under low pressure and high-temperature conditions as per NCERT exemplar Class 11 Physics solutions chapter 13.

    · Lastly, learners should pay attention to the Maxwell and Boltzmann law of velocity and energy distribution. In this, the root means square and average velocity is discussed, of the gaseous particles which act under proportional kinetic energy and temperature.

    NCERT Exemplar Class 11 Solutions

    Check Class 11 Physics Chapter-wise Solutions

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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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    Linguist

    Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning). 

    Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian

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    Production Manager

    Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers. 

    Resource Links for Online MBA 

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    Product Manager

    A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

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    Quality Controller

    A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

    A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

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    Production Engineer

    A career as Production Engineer is crucial in the manufacturing industry. He or she ensures the functionality of production equipment and machinery to improve productivity and minimize production costs in order to drive revenues and increase profitability. 

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    Automation Test Engineer

    An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process. 

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    Product Designer

    Individuals who opt for a career as product designers are responsible for designing the components and overall product concerning its shape, size, and material used in manufacturing. They are responsible for the aesthetic appearance of the product. A product designer uses his or her creative skills to give a product its final outlook and ensures the functionality of the design. 

    Students can opt for various product design degrees such as B.Des and M.Des to become product designers. Industrial product designer prepares 3D models of designs for approval and discusses them with clients and other colleagues. Individuals who opt for a career as a product designer estimate the total cost involved in designing.

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    R&D Personnel

    A career as R&D Personnel requires researching, planning, and implementing new programs and protocols into their organization and overseeing new products’ development. He or she uses his or her creative abilities to improve the existing products as per the requirements of the target market.

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    Commercial Manager

    A Commercial Manager negotiates, advises and secures information about pricing for commercial contracts. He or she is responsible for developing financial plans in order to maximise the business's profitability.

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    Product Manager

    A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

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    ITSM Manager

    ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks. 

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    Information Security Manager

    Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

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    Computer Programmer

    Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

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    Computer System Analyst

    Individuals in the computer systems analyst career path study the hardware and applications that are part of an organization's computer systems, as well as how they are used. They collaborate closely with managers and end-users to identify system specifications and business priorities, as well as to assess the efficiency of computer systems and create techniques to boost IT efficiency. Individuals who opt for a career as a computer system analyst support the implementation, modification, and debugging of new systems after they have been installed.

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    Test Manager

    A Test Manager is a professional responsible for planning, coordinating and controlling test activities. He or she develops test processes and strategies to analyse and determine test methods and tools for test activities. The test manager jobs involve documenting tests that have been carried out, analysing and evaluating software quality to determine further recommended procedures. 

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    Azure Developer

    A career as Azure Developer comes with the responsibility of designing and developing cloud-based applications and maintaining software components. He or she possesses an in-depth knowledge of cloud computing and Azure app service. 

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    Deep Learning Engineer

    A Deep Learning Engineer is an IT professional who is responsible for developing and managing data pipelines. He or she is knowledgeable about analyzing and storing data collected from various sources.  A Career as a Deep Learning Engineer needs to help the  data scientists and analysts to create effective data sets.

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