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

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

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

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

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

Two identical containers $\mathrm{A}$ and $\mathrm{B}$ have frictionless pistons. They contain the same volume of a ideal gas at the same temperature. The mass of the gas in $\mathrm{A}$ is $\mathrm{m}_{\mathrm{A}}$ and that in $\mathrm{B}$ is $\mathrm{mB}$. The gas in each cylinder is now allowed to expand isothermally to double the initial volume. The changes in the pressure in A and B are found to be $\Delta p$ and $1.5 \Delta p$ respectively.

$4 \mathrm{~mA}_{\mathrm{A}}=9 \mathrm{mB}$

$2 \mathrm{~m}_{\mathrm{A}}=3 \mathrm{mB}$

$9 \mathrm{~mA}_{\mathrm{A}}=4 \mathrm{mB}$

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NEET • PHYSICS • KINETIC THEORY OF GASES

Kinetic theory of gases practice · Medium

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Showing 1-30 of 69 questions

1 Medium

1 of 69

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 69

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 Medium

3 of 69

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.

4 Medium

4 of 69

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}

5 Medium

5 of 69

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

6 Medium

6 of 69

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

7 Medium

7 of 69

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

8 Medium

8 of 69

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.

9 Medium

9 of 69

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.

10 Medium

10 of 69

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}

11 Medium

11 of 69

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}}

12 Medium

12 of 69

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.

13 Medium

13 of 69

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.

14 Medium

14 of 69

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.

15 Medium

15 of 69

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.

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16 Medium

16 of 69

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.

17 Medium

17 of 69

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.

18 Medium

18 of 69

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.

19 Medium

19 of 69

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.

20 Medium

20 of 69

Analyzing +4 | -1

Two identical containers

\mathrm{A}

and

\mathrm{B}

have frictionless pistons. They contain the same volume of a ideal gas at the same temperature. The mass of the gas in

\mathrm{A}

\mathrm{m}_{\mathrm{A}}

and that in

\mathrm{B}

\mathrm{mB}

. The gas in each cylinder is now allowed to expand isothermally to double the initial volume. The changes in the pressure in A and B are found to be

\Delta p

and

1.5 \Delta p

respectively.

View answer and explanation

Correct option: C

3 \mathrm{~mA}_{\mathrm{A}}=2 \mathrm{mB}

Option C (

3 \mathrm{~mA}=2 \mathrm{mB}

) is correct because it relates the masses based on the changes in pressure during isothermal expansion using the ideal gas law.

21 Medium

21 of 69

Analyzing +4 | -1

Assertion:

{V}_{\mathrm{rms}}

and

{V}_{\mathrm{mean}}

of gaseous molecules is nearly of the order of velocity of sound.
Reason: The sound travels in air because of vibrational molecular motion.

View answer and explanation

Correct option: B

If both Assertion and Reason are true, but Reason is not the correct explanation of Assertion

Option B is correct because both the assertion and reason are true, but the reason is not the correct explanation of the assertion. RMS and mean speeds are of the order of sound speed, but sound travels due to pressure variations, not vibrational motion.

22 Medium

22 of 69

Understanding +4 | -1

In the absence of intermolecular forces of attraction, the observed pressure

p

will be

View answer and explanation

Correct option: C

> p

Option C (

> p

) is correct because intermolecular forces of attraction reduce the pressure exerted by the gas, so their absence would result in a higher observed pressure.

23 Medium

23 of 69

Application +4 | -1

The root mean square speed of molecules of a gas is 1260 m/s. The average speed of the gas molecules is

View answer and explanation

Correct option: A

1161 m/s

Option A (1161 m/s) is correct because the average speed is related to the RMS speed by a constant factor derived from the Maxwell-Boltzmann distribution.

24 Medium

24 of 69

Application +4 | -1

If number of molecules of

{H_2}

are double than that of

{O_2},

then ratio of kinetic energy of hydrogen and that of oxygen at

300\;K

View answer and explanation

Correct option: A

1\;:1

Option A (

1:1

) is correct because the average kinetic energy depends only on temperature, which is the same for both gases.

25 Medium

25 of 69

Application +4 | -1

The value closest to the thermal velocity of a Helium atom at room temperature (300K) in

m{s^{ - 1}}

\left[ {{k_B} = 1.4 \times {{10}^{ - 23}}J/K;{m_{He}} = 7 \times {{10}^{ - 27}}kg} \right]

View answer and explanation

Correct option: D

1.3 \times {10^3}

Option D (

1.3 \times {10^3}

) is correct because it is the closest value to the calculated thermal velocity of a Helium atom at room temperature.

26 Medium

26 of 69

Understanding +4 | -1

At constant pressure, which of the following is true?

View answer and explanation

Correct option: D

v \propto \frac{1}{{\sqrt \rho }}

Option D (

v \propto \frac{1}{{\sqrt \rho }}

) is correct because at constant pressure, the volume is inversely proportional to the square root of the density.

27 Medium

27 of 69

Application +4 | -1

Two gases

A

and

B

having same pressure

p

, volume

V\;

and absolute temperature

T

are mixed. If the mixture has the volume and temperature as

V

and

T

respectively, then the pressure of the mixture is

View answer and explanation

Correct option: A

2p

Option A (

2p

) is correct because when two gases with the same pressure, volume, and temperature are mixed, the total number of moles doubles, resulting in double the pressure.

28 Medium

28 of 69

Remembering +4 | -1

The rate of diffusion is

View answer and explanation

Correct option: D

Faster in gases than in liquids and solids

The correct answer is D (Faster in gases than in liquids and solids) because diffusion is fastest in gases due to higher kinetic energy and larger intermolecular spaces.

29 Medium

29 of 69

Remembering +4 | -1

The specific heat of an ideal gas is

View answer and explanation

Correct option: D

Independent of

T

Option D (Independent of

T

) is correct because the specific heat of an ideal gas is a constant value that does not depend on temperature.

30 Medium

30 of 69

Analyzing +4 | -1

To raise the temperature of a certain mass of gas by

5{\mathrm{0}^\mathrm{o}}\mathrm{C}

at a constant pressure, 160 cal of heat is required. When the same mass of gas is cooled by

10{\mathrm{0}^\mathrm{o}}\mathrm{C}

at constant volume, 240 cal of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

View answer and explanation

Correct option: C

Option C (6) is correct because the gas has 6 degrees of freedom, calculated from the given heat capacities at constant pressure and volume.

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