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Consider the number of molecules of an ideal gas present per unit volume to be $10^{30}$ and their average velocity to be $2 \times 10^{4} m / s$ . Calculate the rate of collisions of its molecule if its diameter is $7 \times 10^{- 10} m$ .

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Important Questions on Kinetic Theory of Gases

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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

)

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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:

$(γ = \frac{C_{P}}{C_{v}})$

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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 of Gases>Pressure of a Gas

A spring - block system is resting on a frictionless floor as shown in the figure. The spring constant is

2.0 N m^{- 1}

and the mass of the block is

2 .0 kg

. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass

1.0 kg

moving with a speed of

2 .0 m s^{- 1}

collides elastically with the first block. The collision is such that the

2.0 kg

block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is _________.

Question Image

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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:

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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)

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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 of Gases>Pressure of a Gas

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 of Gases>Pressure of a Gas

N molecules each of mass m of a gas

A

and

2 N

molecules each of mass

2 m

of gas

B

are contained in the same vessel which is maintained at temperature

T

. The mean square velocity of molecules of

B

type is

v^{2}

and the mean square rectangular component of the velocity of

A

type is denoted by

ω^{2}

. Then the value of

ω^{2} / v^{2}

is -

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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}]

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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 of Gases>Pressure of a Gas

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 of Gases>Pressure of a Gas

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:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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

r

’) is inversely proportional to:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

A mixture of 2 moles of helium gas (atomic mass = 4u)

,

and 1 mole of argon gas (atomic mass = 40 u) is kept at

300 K

in a container. The ratio of their rms speeds

[\frac{V_{r m s} (h e l i u m)}{V_{r m s} (a r g o n)}],

is close to:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

Which of the following shows the correct relationship between the pressure

' P'

and density

ρ

of an ideal gas at constant temperature ?

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Pressure of a Gas

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

Consider the number of molecules of an ideal gas present per unit volume to be 1030 and their average velocity to be 2×104 m/s. Calculate the rate of collisions of its molecule if its diameter is 7×10-10 m.

Important Questions on Kinetic Theory of Gases

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Consider the number of molecules of an ideal gas present per unit volume to be $10^{30}$ and their average velocity to be $2 \times 10^{4} m / s$ . Calculate the rate of collisions of its molecule if its diameter is $7 \times 10^{- 10} m$ .