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Degree Of Freedom - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • 12 Questions around this concept.

Solve by difficulty

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains
neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride
(polyatomic). Arrange these on the basis of their root mean square speed \mathrm{(v_{rms}) }and choose the correct answer
from the options given below :

For a gaseous expansion, the amount of work done is \mathrm{n(>1)} times less than the heat supplied. The degree of freedom of a gas molecule is equal to,

Two mole of argon are mixed with one mole of hydrogen, then \mathrm{C_{p} / C_{v}} for the mixture is nearly

Concepts Covered - 1

Degree of Freedom

Degree of freedom-

The degree of freedom of systems is defined as the possible independent motions, systems can have.

Or 

The degree of freedom of systems is defined as the number of independent coordinates required to describe the system completely.

The independent motions can be translational, rotational or vibrational or any combination of these.

So the degree of freedom is of three types :
(i) Translational degree of freedom
(ii) Rotational degree of freedom
(iii) Vibrational degree of freedom

The degree of freedom is denoted by f.

And it is given by

f= 3N-R

Where 

N=no.\: of \: particle

R=no.\: of \:relation

  • Value of degree of freedom for

1.Monoatomic gas- 

A monoatomic gas can only have a translational degree of freedom.

I.e f=3

Example- He, Ne, Ar

2. Diatomic gas

A diatomic gas can have three translational degrees of freedom and two rotational degrees of freedom.

I.e  f= 5

Example- H2 , O2 , N2

3. Triatomic gas

A triatomic gas can have three translational degrees of freedom and three rotational degrees of freedom.

I.e  f= 6

Example- H2O

  • Note-

The above degrees of freedom are shown at room temperature. Further at high temperature, in the case of diatomic or polyatomic molecules,
the atoms within the molecule may also vibrate with respect to each other. In such cases, the molecule will have 2 additional degrees of freedom, due to vibrational motion. I.e One for the potential energy and one for the kinetic energy of vibration.

So A diatomic molecule that is free to vibrate (in addition to translation and rotation) will have 7 degrees of freedom.

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Reference Books

Degree of Freedom

Physics Part II Textbook for Class XI

Page No. : 327

Line : 42

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