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Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Document Description: Kinetic Theory of Gases: Assignment for Physics 2022 is part of Kinetic Theory of Gases for Kinetic Theory & Thermodynamics preparation. The notes and questions for Kinetic Theory of Gases: Assignment have been prepared according to the Physics exam syllabus. Information about Kinetic Theory of Gases: Assignment covers topics like and Kinetic Theory of Gases: Assignment Example, for Physics 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Kinetic Theory of Gases: Assignment.

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Q.1. One mole of gas is contained in cube of side 0.2m.if these molecules, each of mass 5 x 10-26kg, moves with translation speed 1 483ms-1 ,calculate the pressure exerted by the gas on the side of cube .

Time interval between successive collision .Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics =  4.83 x1023 N-S

Force exerted for one molecule Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 0.582 x 10-19N

Total force exerted by one mole gas is ( 6 x1023 ) x ( 0.582 x 10-19 N ) = 3.49 x 104N

Average pressure is givenKinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 2.95 x 105 NM-2


Q.2. Calculate the fraction of gas molecules which have the mean–free path in the range λ to 2λ .

The fraction of gas molecules that do not undergoes collision after path length x is Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics. Therefore the fraction of molecules that has free path values between  λ to 2λ is

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 0.37 - 0.14 = 0.23


Q.3. The molecules of a gas move an average speed of 1 450ms-1 . If  η = 16.6 x 10-6 Nsm-2, ρ = 1.25kgm-3 and n = 2.7 x 1025 m-3. Calculate the mean free path and diameter of the gas molecules.

We can write as

λ = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

On inserting the given numerical values, we get

λ = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 8.85 x 10-8m

λ = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

We can invert this relation to express d in terms of λ :

d = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 3.42 x 10-10m


Q.4. (a) Three closed vessel A, B and C at the same temperature T and contains gases which obey the MB distribution of velocities. Vessel A contains only O2 , B only N2 and C a mixture of equal quantities O2 and N2 . If the average speed of the O2 molecules in vessel A is v1 , that of N2 molecules in vessel B in v2 , calculate the average speed of the molecules in vessel C

(b) The temperature of an ideal gas is increased from 120K to 480K . The rms velocity of the gas molecules is v , at 480K Calculate the rms velocity of the gas molecule.

(a) The average speed of molecules of an ideal gas is given by

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics for same gas.

Since, the percentage of A & C are same, average speed of O2 molecules will be equal in A & C i.e. v1 .

(b) Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

= Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

v1 = 2v


Q.5. (a) Two identical containers A and B with friction less pistons contain the same ideal gas at the same temperature and same volume V . The mass of the gas in A is mA and that in B is mB . The gas in each cylinder is allowed to expand isothermally to the same volume 2V . The changes in the pressure in A & B are found to be ΔP and 1.5ΔP respectively. Then find the ratio Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

(b) Find the ratio of the speeds of sound in nitrogen gas to that in helium gas, at 300K

(a) Process is isothermal. Therefore, T = constt × Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics volume is increasing, therefore pressure will decrease. 

In Chamber (A)

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

= Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

In Chamber (B) Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

= Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

From (1) & (2) 

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

3mA = 2mB

(b) v = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

= Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

= √3/5


Q.6. Plot the Density of states as a function of energy and momentum in three, two and one dimensional systems.

(a) 3D

(b) 2D

(c) 1D

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics



Q.7. In the interstellar space, the density of hydrogen molecule H2 is about one molecule / cm3 .Taking the diameter of H2 approximately 1A0 , calculate

(a) Average velocity of the molecule at kinetic temperature is 100K

(b) Mean free path of the Hmolecules

(c) Collision frequency

ρ = 1 molecule / cm3 diameter d = 1A0 T = 300K

m  = 2x (1.67 x 10-24) = 3.34 x 10-24 gm

(a) Average velocity 

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 1 x 105cm/sec

(b)  Mean free path λ = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 2 x 1015 cm

(c) v = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 2 collision per second


Q.8. The mean free path of the molecules of a gas at a pressure p and temperature T is 3x107m . Calculate the mean free path if 

(a) the temperature is doubled and 

(b) the pressure is doubled.

(a) We know

λ = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

When the temperature is doubled, we note that the mean free path will increase by a factor of two. Hence, 

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 6 x10-7 m

(b) When the pressure is doubled, the mean free path will be halved:

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 1.5 x10-7 m


Q.9. (a) At the room temperature, the rms speed of the molecules of a certain diatomic gas is found to be 1930m/ s . What is the name of the gas?

(b) If one mole of a monatomic gas (γ = 5/ 3) is mixed with one mole of a diatomic gas (γ = 7/ 5) . Calculate the value of γ for the mixture?

(a) Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 300K

1930m/s = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

M = 2 g/ mol or the gas is H.

(b) γ1 = 5/3 means gas monatomicKinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

γ2 = 7/5 means gas diatomic Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Cv (for mixture) = Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

= Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Cp = Cv + R = 3R

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 1.5


Q.10. (a) The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300K are 6.21x10-21 J & 484m/ s respectively. The corresponding values at 600K are nearly (assuming ideal gas behavior)

(b) The average translational energy of O2 (molar mass 32) molecules at a particular

temperature is 0.048eV . Calculate the translation K.E. of N2 (molar mass 28 ) molecules in eV at the same temperature?

(c) A vessel contains 1mole of O2 gas (molar mass 32) at a temperature T . The pressure of the gas is P' . An identical vessel containing one mole of the gas (molar mass 4 ) at a temperature 2T , Calculate the pressure.

(d) A vessel contains a mixture of one mole of O2 & two moles of N2  at 300K .

Calculate the ratio of the average rotational kinetic energy per O2  molecule to per Nmolecule.

(a) Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = √2

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics = 684.37m/s

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

K.E = 6.21 x 2 x10-21 J

= 12.42 x 10-21 J

(b) Average translational energy of an ideal gas molecule is 3/2kT which depends on temperature only, Therefore if same temperature 0.048eV

(c) PV = μ RT

Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics

P ∝ T

P' = 2P

(d) Average kinetic energy per molecule per degree of freedom= 1/2kT. Since, both the 

gases are diatomic and at same temperature ( 300K ), both will have same rotational DOF = 2 therefore, both the gases will have the same average rotational K ×E× per molecule

=Kinetic Theory of Gases: Assignment Notes | Study Kinetic Theory & Thermodynamics - Physics= kT

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