physics : class11 Degrees of Freedom : Internal Energy : Thermodynamics MCQ Questions and Answers
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Degrees of Freedom
MCQ questions and answers.
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MCQ Questions
1. How many translational degrees of freedom does a molecule have in three-dimensional space?
A.
1
B.
2
C.
3
D.
6
Correct Answer:
3
Explanation:
A molecule can translate independently along the x-, y-, and z-directions, giving it 3 translational degrees of freedom.
2. A monatomic gas atom is considered to have how many degrees of freedom at ordinary temperatures?
A.
1
B.
2
C.
3
D.
5
Correct Answer:
3
Explanation:
A monatomic gas particle has three translational degrees of freedom and normally does not contribute rotational degrees of freedom.
3. A diatomic gas molecule, neglecting vibrational motion, generally has how many degrees of freedom at ordinary temperatures?
A.
3
B.
4
C.
5
D.
6
Correct Answer:
5
Explanation:
A diatomic molecule has 3 translational and 2 rotational degrees of freedom when vibrational motion is neglected, making a total of 5.
4. Which type of motion contributes to the translational degrees of freedom of a gas molecule?
A.
Motion about its own axis
B.
Motion along the x, y, and z directions
C.
Vibration of its atoms only
D.
Rotation in one plane only
Correct Answer:
Motion along the x, y, and z directions
Explanation:
Translational motion means movement of the molecule as a whole along the three mutually perpendicular directions.
5. For a molecule with f degrees of freedom, the average energy associated with each degree of freedom is:
A.
kT
B.
1/2 kT
C.
2kT
D.
f kT
Correct Answer:
1/2 kT
Explanation:
According to the equipartition principle, each quadratic degree of freedom contributes an average energy of 1/2 kT per molecule.
6. If a gas molecule has 3 translational and 2 rotational degrees of freedom, what is its total number of degrees of freedom?
A.
2
B.
3
C.
5
D.
6
Correct Answer:
5
Explanation:
The total number of degrees of freedom is the sum of independent translational and rotational degrees of freedom: 3 + 2 = 5.
7. How many rotational degrees of freedom does a linear diatomic molecule have when its vibration is neglected?
A.
1
B.
2
C.
3
D.
5
Correct Answer:
2
Explanation:
A linear diatomic molecule can rotate about two axes perpendicular to its bond axis. Rotation about the bond axis is usually neglected.
8. A gas molecule has 6 active degrees of freedom. What is its average energy per molecule according to the equipartition principle?
A.
kT
B.
2kT
C.
3kT
D.
6kT
Correct Answer:
3kT
Explanation:
The average energy is f/2 kT. For f = 6, the energy is 6/2 kT = 3kT per molecule.
9. Which of the following is not a type of degree of freedom of a gas molecule?
A.
Translational
B.
Rotational
C.
Vibrational
D.
Electrical resistance
Correct Answer:
Electrical resistance
Explanation:
Translational, rotational, and vibrational motions are types of molecular degrees of freedom. Electrical resistance is not a molecular degree of freedom.
10. If the number of active degrees of freedom of each molecule increases, what happens to its average internal energy at the same temperature?
A.
It decreases
B.
It remains zero
C.
It increases
D.
It becomes independent of temperature
Correct Answer:
It increases
Explanation:
The average energy per molecule is f/2 kT, so at the same temperature, increasing the number of active degrees of freedom increases the internal energy.
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