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(A): Vibrational energy of diatomic mole...

(A): Vibrational energy of diatomic molecule corresponding to each degree of freedom is KBT,
(R): For every molecule, vibrational degree of freedom is 2.

A

Both (A) and ( R) are true and (R ) is the correct explanation of (A)

B

Both (A) and (R ) are true and (R ) is not the correct explanation of (A)

C

(A) is true but (R ) is false

D

Both (A) and (R ) are false

Text Solution

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The correct Answer is:
C
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The total energy of molecules is divided equally amongst the various degrees of freedom of a molecule. The distribution of kinetic energy along x, y, z axis are E_(K_(x)), E_(K_(y)), E_(K_(z)) Total K.e =E_(K_(x)) + E_(K_(y)) + E_(K_(z)) Since the motion of molecule is equally probable in all the three directions, therefore E_(K_(x)) = E_(K_(y)) = E_(K_(z)) =1/3 E_(K) =1/3 xx 3/2 kT = 1/2 kT , where k =R/N_(A) = Botzman constant. K.E. = 1/2 kT per molecule or =1/2 RT per mole. In vibration motion, molecules possess both kinetic energy as well as potential energy. This means energy of vibration involves two degrees of fiuedom. Vibration energy =2 xx 1/2kT =2 xx 1/2RT [ therefore two degrees of freedom per mole] If the gas molecules have n_(1) translational degrees of freedom, n_2 rotational degrees of freedom and n_(3) vibrational degrees of freedom, that total energy = n_(1)[(kT)/2] + n_(2) [(kT)/2] + n_(3) [(kT)/2] xx 2 Where 'n' is atomicity of gas. How many total degrees of freedom are present in H_(2) molecules in all types of motions ?

The total energy of molecules is divided equally amongst the various degrees of freedom of a molecule. The distribution of kinetic energy along x, y, z axis are E_(K_(x)), E_(K_(y)), E_(K_(z)) Total K.e =E_(K_(x)) + E_(K_(y)) + E_(K_(z)) Since the motion of molecule is equally probable in all the three directions, therefore E_(K_(x)) = E_(K_(y)) = E_(K_(z)) =1/3 E_(K) =1/3 xx 3/2 kT = 1/2 kT , where k =R/N_(A) = Botzman constant. K.E. = 1/2 kT per molecule or =1/2 RT per mole. In vibration motion, molecules possess both kinetic energy as well as potential energy. This means energy of vibration involves two degrees of fiuedom. Vibration energy =2 xx 1/2kT =2 xx 1/2RT [ therefore two degrees of freedom per mole] If the gas molecules have n_(1) translational degrees of freedom, n_2 rotational degrees of freedom and n_(3) vibrational degrees of freedom, that total energy = n_(1)[(kT)/2] + n_(2) [(kT)/2] + n_(3) [(kT)/2] xx 2 Where 'n' is atomicity of gas. The vibrational kinetic energy of CO_2 molecule is

AAKASH SERIES-KINETIC THEORY OF GASES-EXERCISE-IB(Theoretical Questions)
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  4. (A): Air pressure in a car tyre increases during driving. (R) : Abso...

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  5. (A): If pressure of given mass of an ideal gas is doubled and volume i...

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  6. (A): In the pressure equation P=(1)/(3)av(rms)^(2),the term 'a' repres...

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  7. (A): According to the law of equipartition of energy, internal energy ...

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  8. (A): Different gases at the same conditions of temperature and pressur...

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  9. (A): Equal moles of helium and oxygen gases are given cqual quantities...

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  10. (A): The specific heat of a given mass of a gas in an adiabatic proces...

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  11. (A): For a real gas internal energy depends on its temperature as well...

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  12. (A): The gravitational force between the gas molecules is ineffective ...

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  13. (A): Average velocity of gas molecules is zero. (R): Due to random m...

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  14. (A): At constant volume on increasing temperature the collision freque...

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  15. (A): Two gases with the same average translational kinetic energy have...

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  16. (A): The only difference between mean velocity and mean speed is that ...

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  17. A): Number of air molecules in a room in winter is more than the numbe...

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  18. (A): For an ideal gas, at constant temperature, the product of the pre...

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  19. (A): Vibrational energy of diatomic molecule corresponding to each deg...

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  20. (A): A undamped springp-mass system is simplest free vibration system....

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