Match Column - I and Column - II and choose the correct match from the given choices. Column - I Column - II (A) Root mean square speed of gas molecules ( P ) 1 3 n m v 2 (B) Pressure exerted by ideal gas Q 3 R T M (C) Average kinetic energy of a molecule R 5 2 R T (D) Total internal energy of 1 mol of a diatomic gas S 3 2 k B T

( A ) - ( Q ) , ( B ) - ( P ) , ( C ) - ( S ) , ( D ) - ( R )

( A ) - ( R ) , ( B ) - ( P ) , ( C ) - ( S ) , ( D ) - ( Q )

( A ) - ( Q ) , ( B ) - ( R ) , ( C ) - ( S ) , ( D ) - ( P )

( A ) - ( R ) , ( B ) - ( Q ) , ( C ) - ( P ) , ( D ) - ( S )

EASY

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The mean free path of molecules of a certain gas at STP is $1500 d$ , where $d$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $373 K$ is approximately:

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Important Questions on Kinetic Theory

MEDIUM

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

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>Mean Free Path and RMS Speed

As shown schematically in the figure, two vessels contain water solutions (at temperature $T$ ) of potassium permanganate $({KMnO}_{4})$ of different concentrations $n_{1}$ and $n_{2} (n_{1} > n_{2})$ molecules per unit volume with $Δ n = (n_{1} - n_{2}) ≪ n_{1} .$ When they are connected by a tube of small length $l$ and cross-sectional area $S, {KMnO}_{4}$ starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed $v$ of the molecules is limited by the viscous force $- β v$ on each molecule, where $β$ is a constant. Neglecting all terms of the order ${(Δ n)}^{2}$ . Which of the following is/are correct? ( $k_{B}$ is the Boltzmann constant)

Question Image

EASY

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

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

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.

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

Match Column - I and Column - II and choose the correct match from the given choices.

Column - I	Column - II
(A) Root mean square speed of gas molecules	$(P) \frac{1}{3} n m v^{2}$
(B) Pressure exerted by ideal gas	$(Q) \sqrt{\frac{3 R T}{M}}$
(C) Average kinetic energy of a molecule	$(R) \frac{5}{2} R T$
(D) Total internal energy of $1 mol$ of a diatomic gas	$(S) \frac{3}{2} k_{B} T$

MEDIUM

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

The mean free path

l

for a gas molecule depends upon diameter,

d

of the molecule as:

MEDIUM

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

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

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:

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)

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:

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 ?

EASY

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

r

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

HARD

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

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>Mean Free Path and RMS Speed

The pressure of a gas is proportional to

HARD

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

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>Mean Free Path and RMS Speed

Relationship between pressure

(P)

and kinetic energy (K.E.) of ideal gas is

MEDIUM

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

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>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:

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:

$(γ = \frac{C_{P}}{C_{v}})$

The mean free path of molecules of a certain gas at STP is 1500d, where d is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 K is approximately:

Important Questions on Kinetic Theory

Learn and Prepare for any exam you want !

The mean free path of molecules of a certain gas at STP is $1500 d$ , where $d$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $373 K$ is approximately: