MEDIUM

Earn 100

If temperature of a gas in closed container is doubled, then mean free path of gas molecules will be

50% studentsanswered this correctly

Important Questions on Kinetic Theory of Gases

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

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

The mean free path for a gas at temperature

300 K

and pressure

600

torr is

10^{- 7} m .

The mean free path of the gas at a temperature

400 K

and pressure

200

torr 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)

MEDIUM

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

The mean free path

l

for a gas molecule depends upon diameter,

d

of the molecule as:

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:

EASY

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

r

is the radius of molecules in a gas, then the mean free path of molecules is proportional to

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

MEDIUM

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

Calculate the value of the mean free path

(λ)

for oxygen molecules at temperature

27 ° C

and pressure

1.01 \times 10^{5} Pa

. Assume the molecular diameter

0.3 nm

and the gas is ideal.

(k = 1.38 \times 10^{- 23} J K^{- 1})

HARD

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

A system consists of two types of gas molecules

A

and

B

having the same number density

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

. The diameter of

A

and

B

are

10 A

and

5 A

respectively. They suffer collisions at room temperature. The ratio of average distance covered by the molecule

A

to that of

B

between two successive collisions is ___________

\times 10^{- 2}

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:

MEDIUM

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

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true ?

(A) the mean free path of the molecules decreases

(B) the mean collision time between the molecules decreases.

(D) the mean collision time remains unchanged.

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}]

EASY

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

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

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

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)

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)

HARD

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

According to kinetic theory of gases,

A. The motion of the gas molecules freezes at $0 ° C$ .

B. The mean free path of gas molecules decreases if the density of molecules is increased.

C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.

D. Average kinetic energy per molecule per degree of freedom is $\frac{3}{2} k_{B} T$ (for monoatomic gases).

Choose the most appropriate answer from the options given below

EASY

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

The mean free path for a gas, with molecular diameter

d

and number density

n

can be expressed as:

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:

$(γ = \frac{C_{P}}{C_{v}})$

If temperature of a gas in closed container is doubled, then mean free path of gas molecules will be

Important Questions on Kinetic Theory of Gases

Learn and Prepare for any exam you want !