Match List I with List II: List I List II (A) 3 Translational degrees of freedom (I) Monoatomic gases (B) 3 Translational, 2 rotational degrees of freedoms (II) Polyatomic gases (C) 3 Translational, 2

Question

Match List I with List II:

	List I		List II
(A)	$3$ Translational degrees of freedom	(I)	Monoatomic gases
(B)	$3$ Translational, $2$ rotational degrees of freedoms	(II)	Polyatomic gases
(C)	$3$ Translational, $2$ rotational and $1$ vibrational degrees of freedom	(III)	Rigid diatomic gases
(D)	$3$ Translational, $3$ rotational and more than one vibrational degrees of freedom	(IV)	Nonrigid diatomic gases

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TestHub · Accepted Answer

The formula for degree of freedom is given by
$f = 3 N - k$
where $N$ is the number of particles, $k$ is the individual relationship in the system.
For a monoatomic gas particle, $N = 1, k = 0$ . So, $f = 3$
Hence, monoatomic gas has $3$ translational degree of freedom.
For a rigid diatomic gas molecule, there are $5$ degrees of freedom, $3$ translational and $2$ rotational. A diatomic gas can have two extra degrees of freedom due to rotation along two independent axes.
A non rigid diatomic molecule has one extra degree of freedom than a rigid one. This is the vibrational degree of freedom. Hence, it has $6$ degrees of freedom.
So, a non rigid diatomic gas has $3$ translational, $2$ rotational and $1$ vibrational degrees of freedom.
A polyatomic gas has more than two atoms per molecule. Hence, the total number of degrees of freedom is $3$ translational, $3$ rotational and more than one vibrational degree of freedom.

Physics - Heat & Thermo Question with Solution | TestHub

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