Question

Degree of freedom for polyatomic gas is
(A) $ \geqslant 4$
(B) $ \geqslant 5$
(C) $ \geqslant 6$
(D) $ \geqslant 7$

Answer 1

Hint: At normal temperature, the number of degrees of freedom for monoatomic gas molecules is 3, diatomic gas molecules is 5 and triatomic gas molecules is 6.

Complete step by step solution:
A gas molecule is always free to move in the 3 dimensional space and can have kinetic energy due to linear motion along any of the axes, hence a gas molecule has 3 translational degrees of freedom.
A monatomic gas molecule is free to rotate about any axis, but due to its small size, rotation about any axis cannot result in rotational kinetic energy and hence rotational degrees of freedom of a monatomic gas molecule is zero.
Since the translational degrees of freedom for all molecules is 3. The total degrees of freedom for a monatomic gas molecule is said to be 3.
A diatomic gas molecule is free to rotate about any axis, but due to its linear shape, the rotation about bond axis cannot result in rotational kinetic energy, but rotation about axis perpendicular to bond axis can have rotational kinetic energy and hence rotational degrees of freedom of a diatomic gas molecule is 2.
Since the translational degrees of freedom for all molecules is 3. The total degrees of freedom for a diatomic gas molecule is said to be 5.
A diatomic molecule can vibrate along the bond axis and thus a vibrational kinetic energy and a vibrational potential energy can also be present for a diatomic molecule. This means that a diatomic molecule can have 5 or 7 degrees of freedom, depending on absence or presence of vibrations, which generally occur at high temperatures.
Similarly, A triatomic gas molecule is free to rotate about any axis, and can have rotational kinetic energy associated with all the three rotations and hence rotational degrees of freedom of a triatomic gas molecule is 3.
Since the translational degrees of freedom for all molecules is 3. The total degrees of freedom for a triatomic gas molecule is said to be 6.
A triatomic molecule can vibrate along different bond axes and thus more than one vibrational kinetic energy and vibrational potential energy can also be present for a triatomic molecule. This means that a diatomic molecule can have 6 or more degrees of freedom, depending on absence or presence of vibrations, which generally occur at high temperatures.

Therefore, the correct answer to the question is option : C

Note: We can remember the following details from the above explanation: All molecules have 3 translational degrees of freedom. Monoatomic molecules have zero, diatomic molecules have 2 and triatomic molecules have 3 rotational degrees of freedom respectively at normal temperatures.