Ncert Exercises & Solutions

Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. The equation in kinetic theory \(PV = \dfrac{2}{3}E,\) \(E\) is:

1.	the total energy per unit volume.
2.	only the translational part of energy because rotational energy is very small compared to translational energy.
3.	only the translational part of the energy because during collisions with the wall, pressure relates to change in linear momentum.
4.	the translational part of the energy because rotational energies of molecules can be of either sign and its average over all the molecules is zero.

Hint: Use the concept of the kinetic theory of gas molecules.

Explanation: For diatomic molecules like hydrogen, energy contributions come from both translational and rotational motion. However, when applying the equation of kinetic theory: \(PV = \frac{2}{3} E\)
Total Energy (E): For diatomic molecules, the energy consists of:
Translational energy: \(\frac{3}{2} k_B T\) (per molecule)
Rotational energy: \(k_B T\) (for two rotational degrees of freedom)
The equation \(PV= \frac{2}{3} E\) only considers translational energy. The pressure of the gas comes from the change in the linear momentum of molecules when they collide with the container walls. Only the translational component of energy contributes to this momentum exchange. The rotational motion does not directly affect pressure, as it doesn't change linear momentum during collisions with the wall.
Thus, the quantity \(E\) in of the equation \(PV = \frac{2}{3} E\) refers only to the translational energy of the gas molecules.
Hence, option (3) is the correct answer.

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