Question

the average value of rotational kinetic energy of 1 mole of Oxygen gas at temperature t will be ?

Answer 1

O₂ is a diatomic molecule . Hence , there are five degree of freedom for 1 mole of O₂ gas .In which 3 translational and 2 rotational .
∴ degree of freedom for 1 mole of O₂ gas , f = 2 [ for rotational motion ]
We know,
Average Rotational Kinetic energy = $\frac{f}{2}\bold{RT}$
Here f is degree of freedom for rotational motion.
∴ average Rotational Kinetic energy = 2/2 RT = RT

Answer 2

Hello Dear.

Here is the answer---

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We know that oxygen gas forms the diatomic molecules. It reacts with the another oxygen atom thus forming O₂.

  For One mole of O₂, there are five degree of freedom.
Out of 5 degree of Freedom, 3 degree are of Transnational, and 2 degree are of Rotational.

 Since, We Have to calculate the rotational kinetic energy of the one mole of O₂ gas,

 Thus, F = 2

Using the Formula,

    Average Rotational Energy = (F/2) RT
                                                =(2/2) RT
                                                = 1 RT


Therefore, Average value of the Rotational Kinetic Energy is 1 RT.


→→→→→→→→→→→→


Hope it helps.


Have a Nice day.