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The root mean square velocity of a perfect gas is

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Important Questions on Kinetic Theory of Gases

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

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.

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

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

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

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

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

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:

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:

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

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?

EASY

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

The RMS speed of oxygen at room temperature is about

500 m s^{- 1}

. The RMS speed of hydrogen at the same temperature is about

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

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

MEDIUM

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

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 of Gases>Pressure of a Gas

The root mean square speed of smoke particles each of mass

5 \times 10^{- 17} k g

in their Brownian motion in air at

N . T . P

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:

$(γ = \frac{C_{P}}{C_{v}})$

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:

The root mean square velocity of a perfect gas is

Important Questions on Kinetic Theory of Gases

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