Engineering Physics Questions and Answers – Maxwell Boltzmann Statistics

This set of Engineering Physics Multiple Choice Questions & Answers (MCQs) focuses on “Maxwell Boltzmann Statistics”.

1. Phase space is a ________
a) 3 Dimensional Space
b) 4 Dimensional Space
c) 5 Dimensional Space
d) 6 Dimensional Space
View Answer

Answer: d
Explanation: Phase space is a 6 Dimensional space, consisting of the position in x, y, and z directions and its momentum in these directions.

2. Maxwell-Boltzmann law is for the ________
a) Distinguishable particles
b) Indistinguishable Particles
c) Particles with half integral spin
d) Particles with integral spin
View Answer

Answer: a
Explanation: The Maxwell-Boltzmann statistics is for the distinguishable particles, which are basically the classical particles like atoms and molecules.

3. The Maxwell-Boltzmann law is given by the expression ________
a) \(\frac{1}{e^{(\frac{E}{kT})}} \)
b) \(\frac{1}{e^{(1+\frac{E}{kT})}} \)
c) \(\frac{1}{e^{(α+\frac{E}{kT})}} \)
d) \(\frac{1}{e^{(α+\frac{nE}{kT})}}\)
View Answer

Answer: c
Explanation: The correct expression for the Maxwell-Boltzmann law is \(\frac{1}{e^{(α+\frac{E}{kT})}} \), where k is the Boltzmann constant with value 1.98 X 10-23 J/K and T is the Temperature. The constant α depends on the volume and the temperature of the gas.
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4. Maxwell-Boltzmann statistics cannot be applied to _____________
a) Atoms
b) Molecules
c) Photons
d) Lattice
View Answer

Answer: c
Explanation: Maxwell-Boltzmann can only be applied to particles which are distinguishable. Photons are indistinguishable from one other.

5. The ratio of rms velocity to most probable velocity is ________
a) √3 : √2
b) √2 : √3
c) 3 : 2
d) 2 : 3
View Answer

Answer: a
Explanation: As we know, vrms = \(\sqrt{\frac{3RT}{M}}\, and\, v_p = \sqrt{\frac{2RT}{M}}\). They are derived from Maxwell’s speed distribution law. By dividing them, we get: vrms:vp = √3 : √2
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6. The average kinetic energy associated with each degree of freedom is ________
a) kT
b) 2kT
c) kT/2
d) kT/4
View Answer

Answer: c
Explanation: According to the law of equipartition of energy, the average kinetic energy associated with each degree of freedom is kT/2. The total number of independent quantities are called its degree of freedom.

7. The density of molecules is maximum at which speed?
a) Vrms
b) Vp
c) Vmean
d) Vinst
View Answer

Answer: b
Explanation: Most of the particles are moving with the most probable speed. As the velocity increases further, the density of molecules moving with that particular speed decreases.
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8. What would be the most probable velocity for one Oxygen molecule at 300 K?
a) 612 m/s
b) 714 m/s
c) 798 m/s
d) 821 m/s
View Answer

Answer: b
Explanation: Mass of one Oxygen molecule = 32 g/mol
= 32 X 10-3/6.022 X 1023
= 5.31 X 10-26 Kg
Now,\(V_p = \sqrt{\frac{2kT}{M}}\)
Here, T = 300 K, k = 1.98 X 1023 and M = 32
Therefore, \(V_p = \sqrt{\frac{2X 1.98X 30}{5.31}} \) X 104
= 714 m/s.

9. Mass of A is 4 times that of B. What is the ratio of their mean velocities?
a) 1 : 4
b) 4 : 1
c) 1 : 2
d) 2 : 1
View Answer

Answer: c
Explanation: As we know, mean velocity = \(\sqrt{\frac{8kT}{\pi M}}\)
Now, Ma = 4Mb
Therefore, Va = \(\sqrt{\frac{8kT}{\pi M}}\)
And Vb = \(\sqrt{\frac{8kT}{4\pi M}}\)
Dividing we get: Va : Vb = 1:√4
= 1 : 2.
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10. From the figure, what is the highest temperature?
The highest temperature is T3 for density of particles moving with higher speed increases
a) T1
b) T2
c) T3
d) Insufficient Information
View Answer

Answer: c
Explanation: As we know, as the temperature increases, the maximum velocity of the particle decreases and the density of the particles moving with higher speed increases. Thus, the correct option is T3.

11. The total Kinetic Energy of the gas particles is dependent on Temperature only.
a) True
b) False
View Answer

Answer: b
Explanation: As we know, the total kinetic energy of the gas particles = 3nRT/2. Hence, it depends on temperature as well as the number of moles of the gas particle.

12. As the temperature is increased, molecules moving with lower speed increases.
a) True
b) False
View Answer

Answer: b
Explanation: As the temperature is increased, the number of molecules travelling with lower speeds decreases whereas those travelling with higher speeds increases.

13. What is the Kinetic Energy of 2 g of oxygen at -23℃?
a) 186.2 J
b) 194.86 J
c) 201.45 J
d) 256.32 J
View Answer

Answer: b
Explanation: As we know, KE = 3nRT/2
Here, T = 250 K and R = 8.314 J/K
n = 2/32 = 1/16 mol
Therefore, KE = 3 X 8.314 X 250/32
= 194.86 J.

14. What is the rms speed of methane at 27℃?
a) 450 m/s
b) 532 m/s
c) 678 m/s
d) 745 m/s
View Answer

Answer: c
Explanation: As we know, \(v_{rms} = \sqrt{\frac{3kT}{M}}\)
Here, T = 300 K, k = 1.38 X 10-23 J/K, M = 16/6.022 X 10-26 = 2.65 X 10-26
Therefore, \(v_{rms} = \sqrt{\frac{3X 30 X 1.38}{2.65}}\) X 102
= 678 m/s.

15. Which one of the following is the most probable speed?
The particles are moving when the velocity is B for most probable velocity
a) A
b) B
c) C
d) D
View Answer

Answer: b
Explanation: As we know, the most probable speed is the speed at which most of the particles are moving. Thus, as we can see, most of the particles are moving when the velocity is B. Thus, it is the most probable velocity.

Sanfoundry Global Education & Learning Series – Engineering Physics.

To practice all areas of Engineering Physics, here is complete set of 1000+ Multiple Choice Questions and Answers.

If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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