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 = $\bold{\frac{f}{2}RT}$
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----

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

     For one mole of O₂, there are 5 Degree of Freedom.

Out of 5 degree of freedom, 2 degree are of Rotational and 3 degree are of Transnational.

Since, We have to calculate the rotational kinetic energy of 1 mole of O₂ gas,
                             
                 F = 2 

Thus, using the formula, 
         Average Rotational Energy = (F/2) RT
                                                     = (2/2) RT
                                                     = 1 RT.

Thus, the average value of the rotational kinetic energy is 1 RT.


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Hope it helps.


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