The average thermal energy for a mono-atomic gas is: (${{\rm{k}}_{\rm{B}}}$ is Boltzmann constant and ${\rm{T}}$, absolute temperature)

$\frac{3}{2}\,{{\rm{k}}_{\rm{B}}}{\rm{T}}$

$\frac{1}{2}\,{{\rm{k}}_{\rm{B}}}{\rm{T}}$

$\frac{5}{2}\,{{\rm{k}}_{\rm{B}}}{\rm{T}}$

$\frac{7}{2}\,{{\rm{k}}_{\rm{B}}}{\rm{T}}$

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NEET • PHYSICS • KINETIC THEORY OF GASES

Kinetic theory of gases practice · Mixed difficulty

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Showing 1-30 of 115 questions

1 Medium

1 of 115

Remembering +4 | -1

The absolute zero is the temperature at which

View answer and explanation

Correct option: C

Molecular motion ceases

Option C (Molecular motion ceases) is correct because absolute zero (0 Kelvin) is defined as the temperature at which all molecular motion stops.

2 Medium

2 of 115

Analyzing +4 | -1

The internal energy

\left( U \right)

, pressure

\left( p \right)

and volume

\left( V \right)

of an ideal gas are related as

U = 3pV + 4

. The gas is

View answer and explanation

Correct option: B

polyatomic only

Option B (polyatomic only) is correct because the given relation between internal energy, pressure, and volume corresponds to a polyatomic gas.

3 Hard

3 of 115

Analyzing +4 | -1

A monoatomic ideal gas is contained in a rigid container of volume

V

with walls of total inner surface area

A

, thickness

x

and thermal conductivity

K

. The gas is at an initial temperature

T_0

and pressure

P_0

. If the pressure of the gas as a function of time if the temperature of the surrounding air is

T_{\mathrm{s}}

\frac{T_0}{T_0}\left[T_s-\left(\mathrm{T}_s-T_0\right)_e \frac{-Z k A}{3 x R} t\right]

. Find the value of

z

. All temperatures are in absolute scale.

View answer and explanation

Correct option: A

Option A (2) is correct because the pressure of the gas as a function of time depends on the heat transfer rate, which is proportional to the surface area and thermal conductivity.

4 Medium

4 of 115

Analyzing +4 | -1

Assertion: The change in air pressure effect the speed of sound.
Reason: The speed of sound in a gas is proportional to the square of pressure.

View answer and explanation

Correct option: D

If both Assertion and Reason are false

Option D is correct because the speed of sound is independent of pressure, and the speed of sound is proportional to the square root of temperature, not the square of pressure.

5 Hard

5 of 115

Application +4 | -1

The rms speed of oxygen molecule in a vessel at particular temperature is

\left(1+\frac{\gamma}{28}\right)^{\frac{1}{2}} v,

where

v

is the average speed of the molecule. The value of

\gamma

will be:

\left(\pi=\frac{22}{7}\right)

View answer and explanation

Correct option: D

Option D (5) is correct because by equating the given RMS speed with the standard RMS speed formula, we can solve for gamma (

\gamma

6 Hard

6 of 115

Application +4 | -1

For an ideal gas the instantaneous change in pressure

p

with volume

V

is given by the equation

\frac{{dp}}{{dV}}\, = \, - ap.

p\, = \,{p_0}

V\, = \,0

is the given boundary condition, then the maximum temperature one mole of gas can attain is (Here

R

is the gas constant)

View answer and explanation

Correct option: A

\frac{{{p_0}}}{{aeR}}

Option C (A and B only) is correct. The r.m.s velocity depends only on temperature and molar mass, which are the same for both vessels. The pressure is directly proportional to the number of molecules when volume and temperature are constant.

7 Medium

7 of 115

Analyzing +4 | -1

The equation of state of a gas is given by

\left( {P + \frac{{a{T^2}}}{V}} \right){V^c} = \left( {RT + b} \right),

where

a,b,c

and

R

are constants. The isotherms can be represented by

P = A{V^m} - B{V^n},

where

A

and

B

depend only on temperature and

View answer and explanation

Correct option: A

m = - c

and

n = - 1

Option A (

m = - c

and

n = - 1

) is correct because rearranging the given equation of state to solve for P results in terms of

V^{-c}

and

V^{-1}

8 Medium

8 of 115

Understanding +4 | -1

For an ideal gas of diatomic molecules

View answer and explanation

Correct option: D

{C_p} = \frac{7}{2}R

Option D (

{C_p} = \frac{7}{2}R

) is correct because for a diatomic molecule,

f = 5

, so

C_p = (f/2 + 1)R = (5/2 + 1)R = 7/2 R

9 Easy

9 of 115

Understanding +4 | -1

Pressure exerted by a gas is:

View answer and explanation

Correct option: D

Directly proportional to the density of the gas

Option D (Directly proportional to the density of the gas) is correct because pressure exerted by a gas is directly proportional to its density.

10 Medium

10 of 115

Application +4 | -1

If rms velocity of a gas is

{V_{rms}} = 1840m/s

and its density

P = 8.99 \times {10^{ - 2}}kg/{m^3}

, Then pressure of the gas will be

View answer and explanation

Correct option: C

1.01 \times {10^5}N/{m^2}

Option C (

1.01 \times {10^5}N/{m^2}

) is correct because the pressure can be calculated directly from the RMS velocity and density using the formula

P = (1/3) \rho V_{rms}^2

11 Easy

11 of 115

Analyzing +4 | -1

Assertion: Maxwell speed distribution graph is symmetric about most probable speed.
Reason: rms speed of ideal gas, depends upon its type (monoatomic, diatomic and polyatomic).

View answer and explanation

Correct option: D

If both assertion and reason are false

Option D is correct because the Maxwell speed distribution graph is asymmetric, and the RMS speed depends on temperature, not the type of gas (monoatomic, diatomic, etc.).

12 Medium

12 of 115

Application +4 | -1

The molar specific heats of an ideal gas at constant pressure and volume are denoted by

{C_P}\,and\,{C_V}

, respectively. If

\gamma = \frac{{{C_P}}}{{{C_{\;v}}}}

and R is the universal gas constant. Then

{C_V}

is equal to

View answer and explanation

Correct option: C

\frac{R}{{\gamma - 1}}

Option C (

\frac{{R}}{{\gamma - 1}}

) is correct because it is derived from the relationship between

C_P

C_V

\gamma

, and R using the formula

C_P - C_V = R

13 Medium

13 of 115

Remembering +4 | -1

For a real gas (van der Waal’s gas)

View answer and explanation

Correct option: B

Critical temperature is

a/Rb

The correct answer is A because the Boyle temperature for a real gas is given by a/Rb, derived from the van der Waals equation.

14 Medium

14 of 115

Application +4 | -1

{N_2}

molecules is 14 times heavier than a

{H_2}

molecule. At what temperature will the rms speed of

{H_2}

molecules be equal to that of

{N_2}

molecule at

{27^0}C

View answer and explanation

Correct option: D

21.4 K

Option D (21.4 K) is correct because the temperature is calculated by equating the rms speeds and solving for the temperature of H2.

15 Medium

15 of 115

Understanding +4 | -1

If the degree of freedom of a gas are

f,

then the ratio of two specific heats

{C_P}/{C_V}

is given by

View answer and explanation

Correct option: A

\frac{2}{f} + 1

Option A (

\frac{2}{f} + 1

) is correct because the ratio of specific heats is given by

\gamma = 1 + \frac{2}{f}

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16 Medium

16 of 115

Remembering +4 | -1

The

r.m.s.

speed of gas molecules is given by

View answer and explanation

Correct option: B

1.73\sqrt {\frac{{RT}}{M}}

Option B (

1.73\sqrt {\frac{{RT}}{M}}

) is correct because the root mean square speed is given by

v_{rms} = \sqrt{\frac{3RT}{M}} = 1.73\sqrt{\frac{RT}{M}}

17 Medium

17 of 115

Understanding +4 | -1

Oxygen and hydrogen are at the same temperature

T

. The ratio of the mean kinetic energy of oxygen molecules to that of the hydrogen molecules will be

View answer and explanation

Correct option: B

1:1

Option B (1:1) is correct because the average kinetic energy of gas molecules depends only on temperature, and both gases are at the same temperature.

18 Easy

18 of 115

Application +4 | -1

The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is :

View answer and explanation

Correct option: A

5.6\,{m^3}

Option A (

5.6\,{m^3}

) is correct because it is the volume occupied by 4.5 kg of water when treated as an ideal gas at STP.

19 Medium

19 of 115

Remembering +4 | -1

The average kinetic energy of a gas molecule at absolute temperature

T

View answer and explanation

Correct option: C

directly proportional to

T

Option C (directly proportional to

T

) is correct because the average kinetic energy of a gas molecule is directly proportional to the absolute temperature.

20 Easy

20 of 115

Understanding +4 | -1

On colliding in a closed container the gas molecules

View answer and explanation

Correct option: A

Transfer momentum to the balls

The correct answer is A because gas molecules transfer momentum to the walls of the container during collisions, which is the basis for gas pressure.

21 Medium

21 of 115

Understanding +4 | -1

{0^0}C

temperature, root mean square speed of which of the following gas will be maximum?

View answer and explanation

Correct option: A

{H_2}

Option A (

{H_2}

) is correct because hydrogen has the lowest molar mass, resulting in the highest rms speed at a given temperature.

22 Medium

22 of 115

Remembering +4 | -1

The root mean square velocity of molecules of gas is

View answer and explanation

Correct option: A

Proportional to square root of temperature

(\sqrt{T})

Option A (Proportional to square root of temperature

(\sqrt{T})

) is correct because the root mean square velocity is directly proportional to the square root of the temperature.

23 Medium

23 of 115

Remembering +4 | -1

According to the kinetic theory of gases the

r.m.s

velocity of gas molecules is directly proportional to

View answer and explanation

Correct option: B

\sqrt T

Option B (

\sqrt T

) is correct because the RMS velocity of gas molecules is directly proportional to the square root of the absolute temperature.

24 Easy

24 of 115

Understanding +4 | -1

Assertion: Specific heat of a gas at constant pressure

C_P

is greater than its specific heat at constant volume

C_V

.
Reason: At constant pressure, some heat is spent in expansion of the gas.

View answer and explanation

Correct option: A

If both assertion and reason are true and reason is the correct explanation of the assertion

Option A (If both assertion and reason are true and reason is the correct explanation of the assertion) is correct because at constant pressure, some heat is used for expansion, hence

C_P > C_V

25 Medium

25 of 115

Understanding +4 | -1

On any planet, the presence of atmosphere implies [

{C_{rms}}

= root mean square velocity of molecules and

{V_e}

= escape velocity

View answer and explanation

Correct option: A

{C_{rms}} < < Ve

Option A (

{C_{rms}} << Ve

) is correct because for a planet to have an atmosphere, the root mean square velocity of the gas molecules must be much less than the escape velocity.

26 Medium

26 of 115

Remembering +4 | -1

The average thermal energy for a mono-atomic gas is: (

{\mathrm{k}_\mathrm{B}}

is Boltzmann constant and

\mathrm{T}

, absolute temperature)

View answer and explanation

Correct option: B

\frac{3}{2}\,{\mathrm{k}_\mathrm{B}}\mathrm{T}

The correct answer is B because the average thermal energy for a mono-atomic gas is (3/2)k_B*T, where k_B is the Boltzmann constant and T is the absolute temperature.

27 Easy

27 of 115

Analyzing +4 | -1

Assertion: The ratio of specific heat gas at constant pressure and specific heat at constant volume for a diatomic gas is more than that for a monatomic gas.
Reason: The molecules of a monatomic gas have more degrees of freedom than those of a diatomic gas.

View answer and explanation

Correct option: D

If both assertion and reason are false

Option D is correct because both the assertion and the reason are false. Diatomic gases have fewer degrees of freedom than monatomic gases, and their specific heat ratio is lower.

28 Medium

28 of 115

Remembering +4 | -1

The ideal gas equation connecting Pressure (P) Volume (V) and absolute temperature (T) is (Where

{K_B}

is the Blotzmann Constant and N is the number of molecules)

View answer and explanation

Correct option: C

\;PV = {K_B}NT

The correct answer is C because the ideal gas equation relates pressure, volume, and temperature using the Boltzmann constant and the number of molecules as PV = Nk_B*T.

29 Easy

29 of 115

Analyzing +4 | -1

Assertion: Equal masses of helium and oxygen gases are given equal quantities of heat. There will be a greater rise in the temperature of helium compared to that of oxygen.
Reason: The molecular weight of oxygen is more than the molecular weight of helium.

View answer and explanation

Correct option: B

If both assertion and reason are true but reason is not correct explanation of the assertion

Option C (The average rotational kinetic energy of a molecule is

\mathrm{mv}^2 / 4

) is false because the average rotational kinetic energy for a diatomic molecule is

RT

, which translates to

mv^2/2

considering two degrees of freedom.

30 Easy

30 of 115

Understanding +4 | -1

Which of the following gases possesses maximum rms velocity, all being at the same temperature?

View answer and explanation

Correct option: D

Hydrogen

Option D (Hydrogen) is correct because rms velocity is inversely proportional to the square root of the molar mass. Hydrogen has the lowest molar mass.

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