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In a gas at STP, if $n$ is the number density of the molecules and $r$ is the radius of the molecule, then the mean free path of the molecule is inversely proportional to

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Important Questions on Kinetic Theory

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

Increase in temperature of a gas filled in a container will lead to

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

A gas molecule of mass

M

at the surface of the earth has kinetic energy equivalent to

0 ° C

. If it were to go up straight without colliding with any other molecules, how high would it rise? Assume that the height attained is much less than the radius of the earth. (

k_{B}

is Boltzmann constant)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

Which of the following shows the correct relationship between the pressure

' P'

and density

ρ

of an ideal gas at constant temperature ?

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

25 \times 10^{- 3} m^{3}

volume cylinder is filled with

1

mol of

O_{2}

gas at room temperature

(300 K)

. The molecular diameter of

O_{2}

, and its root mean square speed, are found to be

0.3 n m

and

200 m s^{- 1}

, respectively. What is the average collision rate (per second) for an

O_{2}

molecule?

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

15 g

mass of nitrogen gas is enclosed in a vessel at a temperature,

27^{o} C

. The amount of heat transferred to the gas, so that

R . M . S .

velocity of molecules is doubled, is about.

[R = 8 .3 J {(K mole)}^{- 1}]

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape their escape velocity from the earth, is closest to:

[

Boltzmann Constant

k_{B} = 1.38 \times 10^{- 23} J / K

Avogadro number

N_{A} = 6.02 \times 10^{26} / k g

Radius of Earth:

6.4 \times 10^{6} m

Gravitational acceleration on Earth

= 10 m s^{- 2}]

HARD

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature

T

. Assuming the gases are ideal, the correct statement(s) is (are)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

H C l

molecule has rotational, translational and vibrational motions. If the rms velocity of

H C l

molecules in its gaseous phase is

\bar{ν}

, m is its mass and

k_{B}

is Boltzmann's constant, then its temperature will be:

HARD

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

The number of gas molecules striking per second per square meter of the top surface of a table placed in a room at

20 ° C

and

1

atmospheric pressure is of the order of (

k_{b} = 1.4 \times 10^{- 23} J K^{- 1}

and the average mass of an air molecule is

5 \times 10^{- 27} kg

)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

A container is divided into two equal part I and II by a partition with small hole of diameter d. The two partitions are filled with same ideal gas, but held at temperature

T_{I} = 150 K

and

T_{I I} = 300 K

by connecting to heat reservoirs. Let

λ_{I}

and

λ_{I I}

be the mean free paths of the gas particles in the two parts such that

d > > λ_{I}

and

d > > λ_{I I} .

Then

\frac{λ_{I}}{λ_{I I}}

is close to.

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

The number density of molecules of a gas depends on their distance r from the origin as,

n (r) = n_{0} e^{- α r^{4}} .

Then the numer of molecules is proportional to:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

The molecules of a given mass of gas have RMS velocity of

200

m s^{- 1}

27^{o} C

and

1.0 \times 10^{5} N m^{- 2}

pressure. When the temperature and pressure of the gas are respectively,

127^{o} C

and

0.05 \times 10^{5} N m^{- 2}

, the r.m.s. velocity of its molecules in

m s^{- 1}

is:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

For given gas at

1 a t m

pressure,

r m s

speed of the molecules is

200 m / s

127 ° C .

2 a t m

pressure and at

227 ° C,

the

r m s

speed of the molecules will be:

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

10^{22}

gas molecules each of mass

10^{- 26}

kg collides with a surface (perpendicular to it) elastically per second over an area

1 m^{2}

with a speed

10^{4} m / s,

the pressure exerted by the gas molecules will be of the order of:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

The mean free path of molecules of a gas (radius ‘

r

’) is inversely proportional to:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

The average kinetic energy of a monoatomic gas molecule kept at temperature

27 ° C

is (Boltzmann constant

k = 1.3 \times 10^{- 23} {JK}^{- 1})

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

The plot that depicts the behavior of the mean free time

τ

(time between two successive collisions) for the molecules of an ideal gas, as a function of temperature

(T),

qualitatively, is: (Graphs are schematic and not drawn to scale)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

The temperature of an ideal gas is increased from

100 K

400 K

. If the

r m s

speed of the gas molecule is

V

100 K

, then at

400 K

it becomes

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

An ideal gas is enclosed in a cylinder at pressure of

2

atm and temperature,

300 K .

The mean time between two successive collisions is

6 \times 10^{- 8} s .

If the pressure is doubled and temperature is increased to

500 K,

the mean time between two successive collisions will be close to:

HARD

Physics>Heat and Thermodynamics>Kinetic Theory>Mean Free Path and RMS Speed

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^{q}$ , where $V$ is the volume of the gas. The value of $q$ is:

$(γ = \frac{C_{P}}{C_{v}})$

In a gas at STP, if n is the number density of the molecules and r is the radius of the molecule, then the mean free path of the molecule is inversely proportional to

Important Questions on Kinetic Theory

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In a gas at STP, if $n$ is the number density of the molecules and $r$ is the radius of the molecule, then the mean free path of the molecule is inversely proportional to